MATH 236 ELAC MATH DEPARTMENT FALL 2017 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 MATH 236 ELAC MATH DEPARTMENT FALL 2017 TEST 1 REVIEW SHORT ANSWER. Write the word or phrse tht best completes ech sttement or nswers the question. 1) The supply nd demnd equtions for certin product re s = 2,500p - 14,500 nd d = 3,000, where p is the price in dollrs. Find the price where supply equls demnd. p 1) Use point-by-point plotting to sketch the grph of the eqution. 2) f(x) = 2x x - 1 2) 3) The point t which compny's costs equls its revenue is the brek-even. C represents cost, in dollrs, of x units of product. R represents the revenue, in dollrs, for the sle of x units. Find the number of units tht must be produced nd sold in order to brek even. C = 15x + 12,000 R = 18x ) Grph the liner eqution nd determine its slope, if it exists. 4) 3x + 5y = 11 4) 5) A smll compny tht mkes hnd-sewn lether shoes hs fixed costs of $320 dy, nd totl costs of $1200 per dy t n output of 20 pirs of shoes per dy. Assume tht totl cost C is linerly relted to output x. Find n eqution of the line relting output to cost. Write the finl nswer in the form C = mx + b. 5) 6) Find the derivtive of y = 3x5-7x 2-4 x 2. 6) 7) Find the verticl symptote(s) of the grph of the given function. f(x) = x (x - 9)(x + 3) 7) 8) Simplify nd express using positive exponents: 4x 2/3 10x -1/4-1 8) Rtionlize the denomintor nd simplify. Assume tht ll vribles represent positive rel numbers. 2 9) 9) ) The expression my be fctored s shown. Find the missing fctor. 17x 4/5 + x -1/5 = x -1/5 ( ) 10) 1

2 11) Solve the inequlity nd express the nswer in intervl nottion: x2-4x x + 5 > 0. 11) 12) In certin city, the cost of txi ride is computed s follows: There is fixed chrge of $2.25 s soon s you get in the txi, to which chrge of $2.45 per mile is dded. Find liner eqution tht cn be used to determine the cost, C, of n x-mile txi ride. 12) 13) Find the eqution of the following line: Enter your eqution in the simplest possible form. 3 2, -4 nd - 3, -4 on the line (in the xy -plne). 2 13) 14) Find the eqution of the following line: Perpendiculr to 3y x = 1; y-intercept is ) Enter your nswer in slope-intercept form. 15) The finncil deprtment of compny tht produces digitl cmers rrived t the following price-demnd function nd the corresponding revenue function: 15) p(x) = x price-demnd R(x) = x p(x) = x(95.4-6x) revenue function The function p(x) is the wholesle price per cmer t which x million cmers cn be sold nd R(x) is the corresponding revenue (in million dollrs). Both functions hve domin 1 x 15. They lso found the cost function to be C(x) = x (in million dollrs) for mnufcturing nd selling x cmers. Find the profit function nd determine the pproximte number of cmers, rounded to the nerest hundredths, tht should be sold for mximum profit. 16) Suppose the cost of producing x items is given by C(x) = x 3 nd the revenue mde on the sle of x items is R(x) = 400x - 10x 2. Find the number of items which serves s brek-even point. 17) The finncil deprtment of compny tht mnufctures portble MP3 plyers rrived t the following dily cost eqution for mnufcturing x MP3 plyers per dy: C(x) = x + x 2. The verge cost per unit t production level of plyers per dy is C(x) = C(x) x. (A) Find the rtionl function C. (B) Grph the verge cost function on grphing utility for 10 x 200. (C) Use the pproprite commnd on grphing utility to find the dily production level (to the nerest integer) t which the verge cost per plyer is minimum. Wht is the minimum verge cost (to the nerest cent)? 16) 17) 2

3 18) Write 3x3 (x -2) 3-2x 2 (x - 2) 4 reduced to lowest terms. (x - 2) 2 with positive exponents only, nd s single frction 19) Find the stndrd form of the eqution of the line pssing through the two points. (2, - 6) nd (- 9, 6) 18) 19) 20) Express s simple frction reduced to lowest terms: b - 1-2b b b 20) Find the vertex form for the qudrtic function. Then find ech of the following: (A) Intercepts (B) Vertex (C) Mximum or minimum (D) Rnge 21) f(x) = x 2 + 4x ) 22) Suppose n object moves long the y-xis so tht its loction is y = f(x) = x 2 + x t time x (y is in meters nd x is in seconds). Find the instntneous velocity t x = 4 seconds. 22) 23) Let C(x) be the cost function nd R(x) the revenue function. Compute the mrginl cost, mrginl revenue, nd the mrginl profit functions. C(x) = x x x + 40,000 R(x) = 450x 23) 24) The totl cost in dollrs of producing x lwn mowers is given by C(x) = 4, x - x ) Find the mrginl verge cost t x = 20, C'(20) nd interpret the result. Sketch possible grph of function tht stisfies the given conditions. 25) f(-1) = -7 ; lim f(x) = -2; x (-1) - lim f(x) x (-1) + = -7 25) 26) If f(t) = 1, then lim x2/3 h 0 f(-8 + h) - f(-8) h equls 26) 27) Use limits to compute f'(1) where f(x) = 1 2-5x. Enter just frction in lowest terms or n integer. 27) 3

4 28) If f(x) = 4x2 + 4x + 5 nd g(x) = 4x - 7, find g(f(x)). 28) Given functions f nd g, determine the domin of f + g. 29) f(x) = 2x x - 4, g(x) = 4 x ) Find the domin of the composite function f g. 30) f(x) = 6 x + 6, g(x) = 18 x 30) 31) Suppose tht the cost C of removing p% of the pollutnts from chemicl dumping site is given by C(p) = $40, p. Cn compny fford to remove 100% of the pollutnts? Explin. 31) Use the properties of limits to help decide whether the limit exists. If the limit exists, find its vlue. 6x ) lim x 13x ) Find the limit, if it exists. 33) Let f(x) = x2-3x Find lim f(x). 33) x + 2 x -2 34) Let f(x) = x 2-16 x + 4 if x > 0 x 2-16 x - 4 if x < 0 34) Find lim f(x). x 0 35) Find: lim x 5 x - 5 x ) 36) Find: d dx 4 x x 36) 37) Find the second derivtive of f(x) = 1 3 x3/2-4 3 x 1/4 + 5x ) 4

5 Answer Key Testnme: MATH236TEST1REVSHEET 1) $6 2) 3) ) slope: ) C = 44x ) y = 9x 2 + 8x -3 7) x = 9, x = ) 2x 11/12 9) ) 17x ) (-5, 0) (4, ) 12) C = 2.45x ) y = -4 14) y = x ) P(x) = -6x x - 150, must sell pproximtely 6.69 million cmers. 16) 10 items 5

6 Answer Key Testnme: MATH236TEST1REVSHEET 17) (A) C(x) = 1500 x (B) x (C) 39; $ ) x 2 (x - 2)(x + 4) 19) 12x + 11y = ) + b - b 21) Stndrd form: f(x) = (x + 2) 2-9 (A) x-intercepts: - 5, 1; y-intercept: -5 (B) Vertex (-2, -9) (C) Minimum: -9 (D) y -9 22) 9 m/s 23) C'(x) = x x R'(x) = 450 P'(x) = x x ) -$10.33; unit increse in production will decrese the verge cost per unit by pproximtely $10.33 t production level of 20 units. 25) 6

7 Answer Key Testnme: MATH236TEST1REVSHEET 26) ) ) 16x2 + 16x ) (-, -2) or (-2, 4) or (4, ) 30) (-, -3) or (-3, 0) or (0, ) 31) No, the cost of removing p% of the pollutnts increses without bound s p pproches ) 13 33) -7 34) 4 35) Does not exist 36) - 16 x x 4 37) 1 4 x -1/ x -7/4 7