Instructor: Elhoussine Ghardi Course: calcmanagementspring2018

Transcription

1 Student: Date: Instructor: Elhoussine Ghardi Course: calcmanagementspring018 Assignment: HW3spring Differentiate the following function. f (x) = f(x) = 7 4x + 9 e x. f(x) = 6 ln x + 5x 7 3. Differentiate the following function. f (x) = f(x) = 3 x + 5 e x 4. Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = ln x ; x = 1 y = 5. Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 7 e x + 1x; x = 0 y = 6. First use the appropriate properties of logarithms to rewrite f(x), and then find f (x). f(x) = 19x + ln 19x Rewrite f(x) using properties of logarithms. f(x) = (Do not simplify.) 7. dy Find. y = 4 log 8x dy = (Simplify your answer.) 1/6

2 8. The salvage value S (in dollars) of a company limosine after t years is estimated to be given by the formula below. Use the formula to answer the questions. S(t) = 600,000(0.9) t What is the rate of depreciation (in dollars per year) after 1 year? $ per year (Do not round until the final answer. Then round to the nearest cent as needed.) What is the rate of depreciation (in dollars per year) after 10 years? $ per year (Do not round until the final answer. Then round to the nearest cent as needed.) What is the rate of depreciation (in dollars per year) after 15 years? $ per year (Do not round until the final answer. Then round to the nearest cent as needed.) 9. An investment of $ 8,000 earns interest at an annual rate of 8% compounded continuously. (A) Find the instantaneous rate of change of the amount in the account after year(s). $ (Round to two decimal places as needed). (B) Find the instantaneous rate of change of the amount in the account at the time the amount is equal to $ 1,500. $ (Round to two decimal places as needed) f(x) = 3x x f(x) = (9x + 4)(5x 8) (Type an exact answer.) 1. x f(x) = x 3 (Type an exact answer.) 13. Find f (x). f(x) = x 5 3x /6

3 14. The total sales of S (in thousands of DVD's) of a certain movie are given by the following formula where t is the number of months since the release of the DVD. Use the formula to answer the questions. 70t S(t) = t a) Find S (t). S (t) = b) Find S(5) and S (5). The value of S( 5) rounded to the nearest hundredth is. The value of S (5) rounded to the nearest hundredth is. What do the values S(5) = 14 and S (5) = 4.48 indicate? A. After 5 months, the total sales are 14,000 DVD's and the sales are increasing at the rate of 4480 DVD's per month. B. After 5 months, the total sales are 14,000 DVD's and the sales are increasing at the rate of 4.48 DVD's per month. C. After 5 months, the total sales are 4480 DVD's and the sales are increasing at the rate of 14 DVD's per month. D. After 5 months, the total sales are 44,800 DVD's and the sales are increasing at the rate of 1400 DVD's per month. c) Use the results from part (b) to estimate the total sales after 6 months. After 6 months, the total sales will be approximately how many DVD's? (Round to the nearest whole number.) 15. Replace? with an expression that will make the equation valid. d 3 4x 7 = 7 3 4x 6? The missing expression is. 16. Replace? with an expression that will make the equation valid. d e x = e x 3 + 4? The missing expression is. 17. Replace? with an expression that will make the equation valid. d 7 1 ln x + 5 = x 7 + 5? The missing expression is. 3/6

4 18. The demand x is the number of items that can be sold at a price of $p. For with respect to x by differentiating implicitly. The rate of change of the price p with respect to the demand x is. x = p 6p + 500, find the rate of change of p 19. Answer the following questions for the price-demand equation. p + 0.0x = 100 (A) Express the demand x as a function of the price p. x = The domain of this function is. (Type an inequality or a compound inequality.) (B) Express the revenue R as a function of price p. R(p) = (C) Find the elasticity of demand, E(p). E(p) = (D) For which values of p is the demand elastic? Inelastic? Elastic on Inelastic on (E) For which values of p is revenue increasing? Decreasing? Increasing on Decreasing on (F) If p = 35 and the price is decreased, will revenue increase or decrease? Revenue will (1) (G) If p = 65 and the price is decreased, will revenue increase or decrease? Revenue will () (1) increase. decrease. () decrease. increase. 0. Use the price-demand equation to determine whether demand is elastic, inelastic, or has unit elasticity at the indicated value of p. x = f(p) = 15,360 0p, p = 16 Is the demand inelastic, elastic, or unit? Choose the correct answer below. Inelastic Unit Elastic 4/6

5 e x x x e x 4. 7x x x + ln 19 + ln x x 7. 4 x ln ,894.68, , x 75x x (x 3) (3x + 4) 5/6

6 t t A. After 5 months, the total sales are 14,000 DVD's and the sales are increasing at the rate of 4480 DVD's per month. 18, x 16. 3x 17. 7x p ,000 50p 0 p p 50p p 100 p (50,100) (0,50) (0,50) (50,100) (1) decrease. () increase. 0. Unit 6/6