MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) y = - 39x - 80 D) y = x + 8 5
|
|
- Linda Flynn
- 6 years ago
- Views:
Transcription
1 Assn Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the equation of the tangent line to the curve when x has the given value. 1) Find the equation of the tangent line to the graph of the function at the given value of x. f(x) = + 5x at x = 4 1) A) y = 13x - 16 B) y = 1 20 x C) y = - 39x - 80 D) y = x ) Find the slope of the secant line joining (2, f(2)) and (3, f(3)) for f(x) = ) A) -55 B) 55 C) 15 D) -15 3) If an object moves along a line so that it is at y = f(x) = 4 + 3x - 4 at time x (in seconds), find the instantaneous velocity function v = f'(x). A) 4x + 3 B) 8x + 3 C) D) ) List the x-values in the graph at which the function is not differentiable. 4) 4) A) x = 0 B) x = -1 C) x = 2 D) x = 1 5) Suppose an object moves along the y-axis so that its location is y = f(x) = + x at time x (y is in meters and x is in seconds). Find the average velocity for x changing from 3 to 3 + h seconds. A) 7 - h m/s B) 12 - h m/s C) 12 + h m/s D) 7 + h m/s 5) Find the equation of the tangent line to the curve when x has the given value. 6) f(x) = -2- ; x = -1 6) A) y = -1x + -1 B) y = -2x C) y = 2x + -1 D) y = -2x - -1 Find the instantaneous rate of change for the function at the value given. 7) Find the instantaneous rate of change for the function f(x) = 5 + x at x = ) A) -41 B) -39 C) -14 D) 6 1
2 8) Suppose an object moves along the y-axis so that its location is y = f(x) = + x at time x (y is in meters and x is in seconds). Find the average velocity (the average rate of change of y with respect to x) for x changing from 2 to 9 seconds. A) 15 m/s B) 12 m/s C) 84 m/s D) 3 m/s 8) 9) Given f(x + h) - f(x) = 4xh + 4h + 2h2, find the slope of the tangent line at x = 4. 9) A) 22 B) 20 C) 16 D) 8 10) Find the slope of the line tangent to the graph of the function at the given value of x. y = x4 + 2x3 + 2x + 2 at x = -3 A) 65 B) -50 C) 67 D) ) 11) Find f'(x) if f(x) = 6x-2 + 8x3 + 11x. 11) A) f'(x) = -12x B) f(x) = -12x C) f'(x) = -12x D) f'(x) = -12x ) Find y' if y = ) A) 1 B) 5 8 x C) 0 D) ) Find the derivative of y = 3x ) A) y = x-3 B) y = 9x-2 + 8x-3 C) y = 9 + 8x-3 D) y = 9 + 8x3 14) Find y' if y = 6x. 14) A) 6 B) x C) 0 D) 15) A pen manufacturer determined that the total cost in dollars of producing x dozen pens in one day is given by: C(x) = x , 0 x 100 Find the marginal cost at a production level of 70 dozen pens and interpret the result. A) The marginal cost is $0.62/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.62. B) The marginal cost is $0.60/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.60. C) The marginal cost is $0.58/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.58. D) The marginal cost is $0.59/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $ ) 2
3 16) An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given by f(t) = 9t3-9t2 + t + 7. Find the velocity at three seconds. A) 192 feet per second B) 190 feet per second C) 109 feet per second D) 197 feet per second 16) 17) Find f'(x) if f(x) = 3x4 + 6x7. 17) A) 4x3 + 7x6 B) 7x3 + 13x6 C) 3x5 + 7x8 D) 12x3 + 42x6 18) Find f'(x) if f(x) = 9x7/ ) A) f'(x) = 63 5 x 2/5-10x B) f'(x) = 63 5 x 2/5-10x C) f'(x) = 63 5 x 6/5-10x D) f'(x) = 63 5 x 6/5-10x 19) According to one theory of learning, the number of items, w(t), that a person can learn after t hours of instruction is given by: 19) w(t) = 15 3 t2, 0 t 64 Find the rate of learning at the end of eight hours of instruction. A) 45 items per hour B) 20 items per hour C) 5 items per hour D) 60 items per hour 20) Find f'(x) for f(x) = 2x5 + 6x8. 20) A) 10x4 + 48x7 B) 10x6 + 48x9 C) 10x D) 2x4 + 6x7 Find y for the given values of x1 and. 21) y = 2x + 3; x = 18, x = ) A) 1 B) 0.5 C) 5 D) ) The concentration of a certain drug in the bloodstream x hr after being administered is approximately C(x) = 7x. Use the differential to approximate the change in concentration as x 9 + changes from 1 to A) 0.83 B) 0.21 C) 0.43 D) ) Find dy. 23) y = x 3x ) A) 9x + 2 3x + 1 dx B) 9x x + 1 dx C) 9x x + 1 dx D) 9x - 2 3x + 1 dx 24) y = 5 + 7x ) A) 10x dx B) 10x + 14 dx C) 10x - 4 dx D) (10x + 7) dx 3
4 25) Evaluate dy and y for y = f(x) = -7x + 5, x = 7, and dx = x = ) A) dy = 3.75; y = 3.5 B) dy = 3.5; y = 3.5 C) dy = 3.5; y = 3.75 D) dy = 3.75; y = ) The total profit from selling x units of doorknobs is P(x) =(6x - 7)(9x - 8). Find the marginal average profit function. A) P(x) = 54x - 56 B) P(x) = 54x -111 C) P(x) = D) P(x) = ) 27) The demand equation for a certain item is p = 14 - x and the cost equation is C(x) = 7, x. 1,000 Find the marginal profit at a production level of 3,000 and interpret the result. A) $16; at the 3,000 level of production, profit will increase by approximately $16 for each unit B) $4; at the 3,000 level of production, profit will increase by approximately $4 for each unit C) $7; at the 3,000 level of production, profit will increase by approximately $7 for each unit D) $14; at the 3,000 level of production, profit will increase by approximately $14 for each unit 27) 28) Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions. C(x) = x x + 50,000 R(x) = 400x A) C'(x) = x P'(x) = x B) C'(x) = x P'(x) = x C) C'(x) = x P'(x) = x ) 29) A company is planning to manufacture a new blender. After conducting extensive market surveys, the research department estimates a weekly demand of 600 blenders at a price of $50 per blender and a weekly demand of 800 blenders at a price of $40 per blender. Assuming the demand equation is linear, use the research department's estimates to find the revenue equation in terms of the demand x. A) R(x) = 80x - x 2 B) R(x) = 80x C) R(x) = 20x + x 2 20 D) R(x) = 80x ) 4
5 30) The total cost to produce x units of paint is C(x) = (5x + 3)(7x + 4). Find the marginal average cost function. A) C(x) = B) C(x) = 70x + 41 x C) C(x) = 35x x D) C(x) = ) 5
Calculus for Business Economics Life Sciences and Social Sciences 13th Edition Barnett SOLUTIONS MANUAL Full download at:
Calculus for Business Economics Life Sciences and Social Sciences 1th Edition Barnett TEST BANK Full download at: https://testbankreal.com/download/calculus-for-business-economics-life-sciencesand-social-sciences-1th-edition-barnett-test-bank/
More informationNotation for the Derivative:
Notation for the Derivative: MA 15910 Lesson 13 Notes Section 4.1 (calculus part of textbook, page 196) Techniques for Finding Derivatives The derivative of a function y f ( x) may be written in any of
More informationAdditional Review Exam 1 MATH 2053 Please note not all questions will be taken off of this. Study homework and in class notes as well!
Additional Review Exam 1 MATH 2053 Please note not all questions will be taken off of this. Study homework and in class notes as well! x 2 1 1. Calculate lim x 1 x + 1. (a) 2 (b) 1 (c) (d) 2 (e) the limit
More informationt g(t) h(t) k(t)
Problem 1. Determine whether g(t), h(t), and k(t) could correspond to a linear function or an exponential function, or neither. If it is linear or exponential find the formula for the function, and then
More informationExam Review. Exam Review
Chain Rule Chain Rule d dx g(f (x)) = g (f (x))f (x) Chain Rule d dx g(f (x)) = g (f (x))f (x) Write all roots as powers Chain Rule d dx g(f (x)) = g (f (x))f (x) Write all roots as powers ( d dx ) 1 2
More informationMATH 105 CHAPTER 2 page 1
MATH 105 CHAPTER 2 page 1 RATE OF CHANGE EXAMPLE: A company determines that the cost in dollars to manufacture x cases ofcdʼs Imitations of the Rich and Famous by Kevin Connors is given by C(x) =100 +15x
More informationMA 162: Finite Mathematics - Chapter 1
MA 162: Finite Mathematics - Chapter 1 Fall 2014 Ray Kremer University of Kentucky Linear Equations Linear equations are usually represented in one of three ways: 1 Slope-intercept form: y = mx + b 2 Point-Slope
More informationMath 1314 Week 6 Session Notes
Math 1314 Week 6 Session Notes A few remaining examples from Lesson 7: 0.15 Example 17: The model Nt ( ) = 34.4(1 +.315 t) gives the number of people in the US who are between the ages of 45 and 55. Note,
More information4.2 Rolle's Theorem and Mean Value Theorem
4.2 Rolle's Theorem and Mean Value Theorem Rolle's Theorem: Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b). If f (a) = f (b), then there is at least one
More informationMath 234 Spring 2013 Exam 1 Version 1 Solutions
Math 234 Spring 203 Exam Version Solutions Monday, February, 203 () Find (a) lim(x 2 3x 4)/(x 2 6) x 4 (b) lim x 3 5x 2 + 4 x (c) lim x + (x2 3x + 2)/(4 3x 2 ) (a) Observe first that if we simply plug
More informationBARUCH COLLEGE MATH 2003 SPRING 2006 MANUAL FOR THE UNIFORM FINAL EXAMINATION
BARUCH COLLEGE MATH 003 SPRING 006 MANUAL FOR THE UNIFORM FINAL EXAMINATION The final examination for Math 003 will consist of two parts. Part I: Part II: This part will consist of 5 questions similar
More informationFinal Exam Sample Problems
MATH 00 Sec. Final Exam Sample Problems Please READ this! We will have the final exam on Monday, May rd from 0:0 a.m. to 2:0 p.m.. Here are sample problems for the new materials and the problems from the
More informationIn a moment, we will look at a simple example involving the function f(x) = 100 x
Rates of Change Calculus is the study of the way that functions change. There are two types of rates of change: 1. Average rate of change. Instantaneous rate of change In a moment, we will look at a simple
More informationMath 103 Sample Final
Math 103 Sample Final October 1, 007 These problems are a sample of the kinds of problems that may appear on the final exam. Some answers are included to indicate what is expected. Problems that require
More informationUsing derivatives to find the shape of a graph
Using derivatives to find the shape of a graph Example 1 The graph of y = x 2 is decreasing for x < 0 and increasing for x > 0. Notice that where the graph is decreasing the slope of the tangent line,
More informationMath 116 Review A ball is thrown upward from the top of a 200-foot cliff. The initial velocity of the ball is 125 feet per
Math 6 Review You may only use a calculator if the problem is labeled calc.. Find the equation of the tangent line that is tangent to the graph of f and parallel to the given line. Page of 5 f x x, line
More informationExample 11: A country s gross domestic product (in millions of dollars) is modeled by the function
Math 1314 Lesson 7 With this group of word problems, the first step will be to determine what kind of problem we have for each problem. Does it ask for a function value (FV), a rate of change (ROC) or
More information( ) 4 ( )! x f) h(x) = 2cos x + 1
Chapter Prerequisite Skills BLM -.. Identifying Types of Functions. Identify the type of function (polynomial, rational, logarithmic, etc.) represented by each of the following. Justify your response.
More informationStudy Guide - Part 1
Math 116 Spring 2015 Study Guide - Part 1 1. Find the slope of a line that goes through the points (1, 5) and ( 3, 13). The slope is (A) Less than -1 (B) Between -1 and 1 (C) Between 1 and 3 (D) More than
More informationTHE USE OF A CALCULATOR, CELL PHONE, OR ANY OTHER ELECTRONIC DEVICE IS NOT PERMITTED DURING THIS EXAMINATION.
MATH 110 FINAL EXAM **Test** December 14, 2009 TEST VERSION A NAME STUDENT NUMBER INSTRUCTOR SECTION NUMBER This examination will be machine processed by the University Testing Service. Use only a number
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Assn.1-.3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) How long will it take for the value of an account to be $890 if $350 is deposited
More informationLab 10: Optimizing Revenue and Profits (Including Elasticity of Demand)
Lab 10: Optimizing Revenue and Profits (Including Elasticity of Demand) There's no doubt that the "bottom line" is the maximization of profit, at least to the CEO and shareholders. However, the sales director
More informationMATH 142 Business Mathematics II
MATH 142 Business Mathematics II Summer, 2016, WEEK 2 JoungDong Kim Week 2: 4.1, 4.2, 4.3, 4.4, 4.5 Chapter 4 Rules for the Derivative Section 4.1 Derivatives of Powers, Exponents, and Sums Differentiation
More informationYou may be given raw data concerning costs and revenues. In that case, you ll need to start by finding functions to represent cost and revenue.
Example 2: Suppose a company can model its costs according to the function 3 2 Cx ( ) 0.000003x 0.04x 200x 70, 000 where Cxis ( ) given in dollars and demand can be modeled by p 0.02x 300. a. Find the
More informationWEEK 1 REVIEW Lines and Linear Models. A VERTICAL line has NO SLOPE. All other lines have change in y rise y2-
WEEK 1 REVIEW Lines and Linear Models SLOPE A VERTICAL line has NO SLOPE. All other lines have change in y rise y- y1 slope = m = = = change in x run x - x 1 Find the slope of the line passing through
More informationWorksheet A ALGEBRA PMT
Worksheet A 1 Find the quotient obtained in dividing a (x 3 + 2x 2 x 2) by (x + 1) b (x 3 + 2x 2 9x + 2) by (x 2) c (20 + x + 3x 2 + x 3 ) by (x + 4) d (2x 3 x 2 4x + 3) by (x 1) e (6x 3 19x 2 73x + 90)
More informationMath 1526 Summer 2000 Session 1
Math 1526 Summer 2 Session 1 Lab #2 Part #1 Rate of Change This lab will investigate the relationship between the average rate of change, the slope of a secant line, the instantaneous rate change and the
More informationMath 116: Business Calculus
Math 116: Business Calculus Instructor: Colin Clark Spring 2017 Exam 1 - Thursday February 9. 1.1 Slopes and Equations of Lines. 1.2 Linear Functions and Applications. 2.1 Properties of Functions. 2.2
More informationThe Trout Pond Revisited
The Trout Pond Revisited A. MATERIALS NEEDED Worksheet, calculator, ruler B. OBJECTIVE The student will use the knowledge already gained concerning the calculations of slopes of lines to find average and
More informationName: Math 10250, Final Exam - Version A May 8, 2007
Math 050, Final Exam - Version A May 8, 007 Be sure that you have all 6 pages of the test. Calculators are allowed for this examination. The exam lasts for two hours. The Honor Code is in effect for this
More informationb) According to the statistics above the graph, the slope is What are the units and meaning of this value?
! Name: Date: Hr: LINEAR MODELS Writing Motion Equations 1) Answer the following questions using the position vs. time graph of a runner in a race shown below. Be sure to show all work (formula, substitution,
More informationFinal Exam Review. b) lim. 3. Find the limit, if it exists. If the limit is infinite, indicate whether it is + or. [Sec. 2.
Final Exam Review Math 42G 2x, x >. Graph f(x) = { 8 x, x Find the following limits. a) lim x f(x). Label at least four points. [Sec. 2.4, 2.] b) lim f(x) x + c) lim f(x) = Exist/DNE (Circle one) x 2,
More informationTest # 4 Review Math MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Test # 4 Review Math 25 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the integral. ) 4(2x + 5) A) 4 (2x + 5) 4 + C B) 4 (2x + 5) 4 +
More informationMLC at Boise State Lines and Rates Activity 1 Week #2
Lines and Rates Activity 1 Week #2 This activity will use slopes to calculate marginal profit, revenue and cost of functions. What is Marginal? Marginal cost is the cost added by producing one additional
More information1/20 2/17 3/14 4/29 5/20 Total/100. Exam II- VERSION I Spring 2011
1/20 2/17 3/14 4/29 5/20 Total/100 Do not write in the spaces above. MATH 150-03 Dr. Morton Exam II- VERSION I Spring 2011 Name: Directions: You have 50 minutes in which to complete this exam. Make sure
More informationS14 Exponential Growth and Decay (Graphing Calculator or App Needed)
1010 Homework Name S14 Exponential Growth and Decay (Graphing Calculator or App Needed) 1. Without graphing, classify each of the following as increasing or decreasing and find f (0). a. f (x) = 1.5(0.75)
More informationLecture 2: Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and
Lecture 2: Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and Constrained Optimization The marginal or derivative function and optimization-basic principles The average function
More informationMLC at Boise State Polynomials Activity 2 Week #3
Polynomials Activity 2 Week #3 This activity will discuss rate of change from a graphical prespective. We will be building a t-chart from a function first by hand and then by using Excel. Getting Started
More informationChapter 2-4 Review. Find the equation of the following graphs. Then state the domain and range: 1a) 1b) 1c)
Chapter - Review Find the equation of the following graphs. Then state the domain and range: a) b) c) a) b) c) a) b) c) Find the domain of the following functions. Write your answer in interval notation:
More informationYou are responsible for upholding the University of Maryland Honor Code while taking this exam.
Econ 300 Spring 013 First Midterm Exam version W Answers This exam consists of 5 multiple choice questions. The maximum duration of the exam is 50 minutes. 1. In the spaces provided on the scantron, write
More informationb. Find an expression for the machine s book value in the t-th year of use (0 < t < 15).
Section 1.5: Linear Models An asset is an item owned that has value. Linear Depreciation refers to the amount of decrease in the book value of an asset. The purchase price, also known as original cost,
More informationMAT Pre-Calculus Class Worksheet - Word Problems Chapter 1
MAT 111 - Pre-Calculus Name Class Worksheet - Word Problems Chapter 1 1. The cost of a Frigbox refrigerator is $950, and it depreciates $50 each year. The cost of a new Arctic Air refrigerator is $1200,
More information1 Economical Applications
WEEK 4 Reading [SB], 3.6, pp. 58-69 1 Economical Applications 1.1 Production Function A production function y f(q) assigns to amount q of input the corresponding output y. Usually f is - increasing, that
More informationSection 9.1 Solving Linear Inequalities
Section 9.1 Solving Linear Inequalities We know that a linear equation in x can be expressed as ax + b = 0. A linear inequality in x can be written in one of the following forms: ax + b < 0, ax + b 0,
More informationSection Linear Functions and Math Models
Section 1.1 - Linear Functions and Math Models Lines: Four basic things to know 1. The slope of the line 2. The equation of the line 3. The x-intercept 4. The y-intercept 1. Slope: If (x 1, y 1 ) and (x
More informationMathematics for Business and Economics - Fall 2015
NAME: Mathematics for Business and Economics - Fall 2015 Final Exam, December 14, 2015 In all non-multiple choice problems you are required to show all your work and provide the necessary explanations
More informationNote: I gave a few examples of nearly each of these. eg. #17 and #18 are the same type of problem.
Study Guide for Exam 3 Sections covered: 3.6, Ch 5 and Ch 7 Exam highlights 1 implicit differentiation 3 plain derivatives 3 plain antiderivatives (1 with substitution) 1 Find and interpret Partial Derivatives
More informationFinal Exam Review - Business Calculus - Spring x x
Final Exam Review - Business Calculus - Spring 2016 Name: 1. (a) Find limit lim x 1 x 1 x 1 (b) Find limit lim x 0 x + 2 4 x 1 2. Use the definition of derivative: dy dx = lim f(x + h) f(x) h 0 h Given
More informationName: Practice B Exam 2. October 8, 2014
Department of Mathematics University of Notre Dame Math 10250 Elem. of Calc. I Name: Instructor: Practice B Exam 2 October 8, 2014 This exam is in 2 parts on 10 pages and contains 14 problems worth a total
More informationMathematics (Project Maths Phase 2)
L.17 NAME SCHOOL TEACHER Pre-Leaving Certificate Examination, 2013 Mathematics (Project Maths Phase 2) Paper 1 Higher Level Time: 2 hours, 30 minutes 300 marks For examiner Question 1 Centre stamp 2 3
More informationPRINTABLE VERSION. Practice Final Exam
Page 1 of 25 PRINTABLE VERSION Practice Final Exam Question 1 The following table of values gives a company's annual profits in millions of dollars. Rescale the data so that the year 2003 corresponds to
More informationRate of Change Problems
.6 Rate of Change Problems Earlier in this chapter, the connection between calculus and physics was examined in relation to velocity and acceleration. There are many other applications of calculus to physics,
More informationMathematical Analysis II- Group Project
Mathematical Analysis II- Group Project Student #1: Last Name First Name Student #2: Last Name First Name Functions used for the project: Price Function: Problem 1 Cost Function: Revenue Function: Problem
More informationBARUCH COLLEGE MATH 2205 SPRING MANUAL FOR THE UNIFORM FINAL EXAMINATION Joseph Collison, Warren Gordon, Walter Wang, April Allen Materowski
BARUCH COLLEGE MATH 05 SPRING 006 MANUAL FOR THE UNIFORM FINAL EXAMINATION Joseph Collison, Warren Gordon, Walter Wang, April Allen Materowski The final examination for Math 05 will consist of two parts.
More informationAssignment 3.3, 3.4, 3.5. Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Assignment 3.3, 3.4, 3.5 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use Descartes' Rule of Signs to determine the possible number of positive
More informationSection 1.2: Linear Functions and Applications
Section 1.2: Linear Functions and Applications Linear function: a function that has constant rate of change (regardless of which 2 points are used to calculate it). It increases (or decreases) at the same
More informationWEEK 2 REVIEW. Straight Lines (1.2) Linear Models (1.3) Intersection Points (1.4) Least Squares (1.5)
WEEK 2 REVIEW Straight Lines (1.2) Linear Models (1.3) Intersection Points (1.4) Least Squares (1.5) 1 STRAIGHT LINES SLOPE A VERTICAL line has NO SLOPE. All other lines have a slope given by m = rise
More informationMathematics Level A. Højere handelseksamen. Friday May 19, 2017 At hhx171-mat/a
Mathematics Level A Højere handelseksamen hhx171-mat/a-19052017 Friday May 19, 2017 At 9.00 14.00 Mathematics A The paper consists of two partial tests. The partial test without Tools consist of the exercises
More informationLecture 11 - Business and Economics Optimization Problems and Asymptotes
Lecture 11 - Business and Economics Optimization Problems and Asymptotes 11.1 More Economics Applications Price Elasticity of Demand One way economists measure the responsiveness of consumers to a change
More informationList the quadrant(s) in which the given point is located. 1) (-10, 0) A) On an axis B) II C) IV D) III
MTH 55 Chapter 2 HW List the quadrant(s) in which the given point is located. 1) (-10, 0) 1) A) On an axis B) II C) IV D) III 2) The first coordinate is positive. 2) A) I, IV B) I, II C) III, IV D) II,
More informationReview Exercise Set 13. Find the slope and the equation of the line in the following graph. If the slope is undefined, then indicate it as such.
Review Exercise Set 13 Exercise 1: Find the slope and the equation of the line in the following graph. If the slope is undefined, then indicate it as such. Exercise 2: Write a linear function that can
More informationMA Lesson 13 Notes Section 4.1 (calculus part of textbook, page 196) Techniques for Finding Derivatives
Notation for the Derivative: MA 15910 Lesson 13 Notes Section 4.1 (calculus part of tetbook, page 196) Techniques for Finding Derivatives The derivative of a function y f ( ) may be written in any of these
More information25 Increasing and Decreasing Functions
- 25 Increasing and Decreasing Functions It is useful in mathematics to define whether a function is increasing or decreasing. In this section we will use the differential of a function to determine this
More informationEXAM #2 Review. Spring Name: MATH 142, Drost Section # Seat #
Spring 2010 1 EXAM #2 Review Name: MATH 142, Drost Section # Seat # 1. Katy s Kitchen has a total cost function of C(x) = x + 25 to make x jars of jam, and C(x) is measured in dollars. The revenue in dollars,
More informationrise m x run The slope is a ratio of how y changes as x changes: Lines and Linear Modeling POINT-SLOPE form: y y1 m( x
Chapter 1 Notes 1 (c) Epstein, 013 Chapter 1 Notes (c) Epstein, 013 Chapter1: Lines and Linear Modeling POINT-SLOPE form: y y1 m( x x1) 1.1 The Cartesian Coordinate System A properly laeled set of axes
More informationIntroduction to the Gains from Trade 1
Introduction to the Gains from Trade 1 We begin by describing the theory underlying the gains from exchange. A useful way to proceed is to define an indifference curve. 2 (1) The idea of the indifference
More informationQuantitative Techniques (Finance) 203. Derivatives for Functions with Multiple Variables
Quantitative Techniques (Finance) 203 Derivatives for Functions with Multiple Variables Felix Chan October 2006 1 Introduction In the previous lecture, we discussed the concept of derivative as approximation
More informationInstructor: Elhoussine Ghardi Course: calcmanagementspring2018
Student: Date: Instructor: Elhoussine Ghardi Course: calcmanagementspring018 Assignment: HW3spring018 1. Differentiate the following function. f (x) = f(x) = 7 4x + 9 e x. f(x) = 6 ln x + 5x 7 3. Differentiate
More informationLab 14: Accumulation and Integration
Lab 14: Accumulation and Integration Sometimes we know more about how a quantity changes than what it is at any point. The speedometer on our car tells how fast we are traveling but do we know where we
More informationMath Fundamental Principles of Calculus Final - Fall 2015 December 14th, 2015
Math 118 - Fundamental Principles of Calculus Final - Fall 2015 December 14th, 2015 Directions. Fill out your name, signature and student ID number on the lines below right now, before starting the exam!
More informationAP CALCULUS AB CHAPTER 4 PRACTICE PROBLEMS. Find the location of the indicated absolute extremum for the function. 1) Maximum 1)
AP CALCULUS AB CHAPTER 4 PRACTICE PROBLEMS Find the location of the indicated absolute extremum for the function. 1) Maximum 1) A) No maximum B) x = 0 C) x = 2 D) x = -1 Find the extreme values of the
More information0 Review: Lines, Fractions, Exponents Lines Fractions Rules of exponents... 5
Contents 0 Review: Lines, Fractions, Exponents 3 0.1 Lines................................... 3 0.2 Fractions................................ 4 0.3 Rules of exponents........................... 5 1 Functions
More informationReview Problems for Mid-Term 1 (MAT1250/Cal Poly Pomona Fall 2018) ( x + 1) 36 [Hint: Find x] x + x x. x 1. = + g.
Prof: M. Nasab Review Problems for Mid-Term (MAT50/Cal Pol Pomona Fall 08). Factor completel 5 +. Find all real zeroes of 8 4 + [Hint: Find ]. Find all real zeroes of ( + ) 6 [Hint: Find ] 4. Add and reduce
More information1.1 Forms for fractions px + q An expression of the form (x + r) (x + s) quadratic expression which factorises) may be written as
1 Partial Fractions x 2 + 1 ny rational expression e.g. x (x 2 1) or x 4 x may be written () (x 3) as a sum of simpler fractions. This has uses in many areas e.g. integration or Laplace Transforms. The
More information: Chain Rule, Rules for Exponential and Logarithmic Functions, and Elasticity
4.3-4.5: Chain Rule, Rules for Exponential and Logarithmic Functions, and Elasticity The Chain Rule: Given y = f(g(x)). If the derivatives g (x) and f (g(x)) both exist, then y exists and (f(g(x))) = f
More informationCalculus Review with Matlab
Calculus Review with Matlab While Matlab is capable of doing symbolic math (i.e. algebra) for us, the real power of Matlab comes out when we use it to implement numerical methods for solving problems,
More informationMA162: Finite mathematics
MA162: Finite mathematics Paul Koester University of Kentucky September 4, 2013 Schedule: First Web Assign assignment due on Friday, September 6 by 6:00 pm. Second Web Assign assignment due on Tuesday,
More informationFinal Examination Re - Calculus I 21 December 2015
. (5 points) Given the graph of f below, determine each of the following. Use, or does not exist where appropriate. y (a) (b) x 3 x 2 + (c) x 2 (d) x 2 (e) f(2) = (f) x (g) x (h) f (3) = 3 2 6 5 4 3 2
More informationMath Review Chapter 1
Math 60 - Review Chapter Name ) A mortgage on a house is $90,000, the interest rate is 8 %, and the loan period is 5 years. What is the monthly payment? ) Joan wants to start an annuity that will have
More information2. Find the marginal profit if a profit function is (2x 2 4x + 4)e 4x and simplify.
Additional Review Exam 2 MATH 2053 The only formula that will be provided is for economic lot size (section 12.3) as announced in class, no WebWork questions were given on this. km q = 2a Please note not
More informationPAPER NO.1 : MICROECONOMICS ANALYSIS MODULE NO.6 : INDIFFERENCE CURVES
Subject Paper No and Title Module No and Title Module Tag 1: Microeconomics Analysis 6: Indifference Curves BSE_P1_M6 PAPER NO.1 : MICRO ANALYSIS TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction
More informationCS 3331 Numerical Methods Lecture 2: Functions of One Variable. Cherung Lee
CS 3331 Numerical Methods Lecture 2: Functions of One Variable Cherung Lee Outline Introduction Solving nonlinear equations: find x such that f(x ) = 0. Binary search methods: (Bisection, regula falsi)
More information^(-y-'h) (-!)-'(-5)- i- i
68 Chapter 1 LINEAR FUNCTIONS The slope 1032.6 indicates that tuition and fees have increased approximately $1033 per year. (c) The year 202 is too far in the future to rely on this equation to predict
More informationUse a graphing calculator to approximate all real solutions of the equation. 1) f(x) = x3-3x2-36x A) 36, 3, 108 B) -6, 3, 6 C) -3, 3, 6 D) 3
Assignment 1 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a graphing calculator to approximate all real solutions of the equation. 1)
More informationPartial Fractions. A rational function is a fraction in which both the numerator and denominator are polynomials. For example, f ( x) = 4, g( x) =
Partial Fractions A rational function is a fraction in which both the numerator and denominator are polynomials. For example, f ( x) = 4, g( x) = 3 x 2 x + 5, and h( x) = x + 26 x 2 are rational functions.
More informationMath Winter 2014 Exam 1 January 30, PAGE 1 13 PAGE 2 11 PAGE 3 12 PAGE 4 14 Total 50
Name: Math 112 - Winter 2014 Exam 1 January 30, 2014 Section: Student ID Number: PAGE 1 13 PAGE 2 11 PAGE 3 12 PAGE 4 14 Total 50 After this cover page, there are 5 problems spanning 4 pages. Please make
More informationPreferences - A Reminder
Chapter 4 Utility Preferences - A Reminder x y: x is preferred strictly to y. p x ~ y: x and y are equally preferred. f ~ x y: x is preferred at least as much as is y. Preferences - A Reminder Completeness:
More informationChapter 4 Partial Fractions
Chapter 4 8 Partial Fraction Chapter 4 Partial Fractions 4. Introduction: A fraction is a symbol indicating the division of integers. For example,, are fractions and are called Common 9 Fraction. The dividend
More informationMath Week in Review #1. Perpendicular Lines - slopes are opposite (or negative) reciprocals of each other
Math 141 Spring 2006 c Heather Ramsey Page 1 Section 1.2 m = y x = y 2 y 1 x 2 x 1 Math 141 - Week in Review #1 Point-Slope Form: y y 1 = m(x x 1 ), where m is slope and (x 1,y 1 ) is any point on the
More informationName Student ID # Instructor Lab Period Date Due. Lab 6 The Tangent
Name Student ID # Instructor Lab Period Date Due Lab 6 The Tangent Objectives 1. To visualize the concept of the tangent. 2. To define the slope of the tangent line. 3. To develop a definition of the tangent
More informationPractice Exam 1. Use the limit laws from class compute the following limit. Show all your work and cite all rules used explicitly. xf(x) + 5x.
Practice Exam 1 Tese problems are meant to approximate wat Exam 1 will be like. You can expect tat problems on te exam will be of similar difficulty. Te actual exam will ave problems from sections 11.1
More informationComparing Multiple Representations. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Warm Up 1. Find the slope of a line through points (3, 4) and (6, 2). -2 3 2. The slope of a line is 2 and the y-intercept is 10. What is the
More informationMATH 1015 Final Exam Review Rev 02/2018
MATH 1 Final Exam Review Rev 0/018 ============================================================================== 1)Find the domain and range for the function. 1) 3 1-7 - - - -3 - -1 1 3 7 - -3 - - - -7
More informationEconomics and Such LRT 02/19/2018
Economics and Such LRT 02/19/2018 1 / 14 Marginal as used in economics Marginal is a word used in economics as a synonym for instantaneous rate of change. Because marginal means some sort of derivative
More informationSection 3.1 Relative extrema and intervals of increase and decrease.
Section 3.1 Relative extrema and intervals of increase and decrease. 4 3 Problem 1: Consider the function: f ( x) x 8x 400 Obtain the graph of this function on your graphing calculator using [-10, 10]
More informationProblem Set 5 Answers. A grocery shop is owned by Mr. Moore and has the following statement of revenues and costs:
1. Ch 7, Problem 7.2 Problem Set 5 Answers A grocery shop is owned by Mr. Moore and has the following statement of revenues and costs: Revenues $250,000 Supplies $25,000 Electricity $6,000 Employee salaries
More informationProblem # 2. In a country with a large population, the number of persons, N, that are HIV positive at time t is given by:
Problem # 1 A marketing survey indicates that 60% of the population owns an automobile, 30% owns a house, and 20% owns both an automobile and a house. Calculate the probability that a person chosen at
More informationTN 2 - Basic Calculus with Financial Applications
G.S. Questa, 016 TN Basic Calculus with Finance [016-09-03] Page 1 of 16 TN - Basic Calculus with Financial Applications 1 Functions and Limits Derivatives 3 Taylor Series 4 Maxima and Minima 5 The Logarithmic
More informationPractice Problem Set 6 Solutions
Economics 370 Professor H.J. Schuetze Practice Problem Set 6 Solutions Read each question in its entirety before beginning, then answer the question as clearly and concisely as possible. Make sure to answer
More informationEconomics 101 Section 5
Economics 101 Section 5 Lecture #10 February 17, 2004 The Budget Constraint Marginal Utility Consumer Choice Indifference Curves Overview of Chapter 5 Consumer Choice Consumer utility and marginal utility
More information