Exam 2 Practice 2

Exam 2 Practice 2 - i . I f f (x) = (U4)x4- + ( 213)x3 (...

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i. If f(x) =(U4)x4- (213)x3 + (5/2)x2 - 6x + 5 then f '(x) is: a) x3 -2x2 +5x -6 b) (l/4)x3- (2/3)x2 + (5/2)x- 6 c) 1,6x3-9x2 4x 6 d) 3x3-2x 7 e) (L/4\xa-(2/3)x3+(5/2\x2 5 Z. If f(x) = xtet" then f a) 2xes' b) zxes' x2e5* c) sxes" d) 2xes' 5x2es* e) 10x2es* 3. If f(x) ln (3x2 + eu) then f a) tn( 6x 2e2") b) (6x + 2eu\ ln(3x2 eb) c) 6x Zeb d) (6x + 2e2)/(3x2 +7 + eu\ e) 1/(3x2 eh) }' 4. If f(x) et' , then f = l-x 1-x '1,-2x L-Zx a) eb b) eo* c) d) e) eo 5. If y x ln(2x), then y'= f a) ln(2x) L/(2x) b) (Llz) + ln(2x) c) 1/(2x) L d) 1 ln(zx) e) None of these 6. If y=f(x) {tf * (Zx)'l [1 + (Zx)']u', then y'=f a) (zx)/ {tr * (2x)'l @x) /{tr 1x1l{tl + (2x)'1 /r/[t zx'] e) (4x){t1 + 4xzf 7. Theequationof thetangentlinetothegraphof f(x)=2x2 -x+10 at x=0 is: a) y=-x+1,0 b) y=x-L0 c) y=10x d) y=10x-1 e) y=10x-L0 8. Suppose f'(x)=0 when x=2 andinaddition f"(x)>0 for x<4 and f'(x)<0 for x>4. Given this information, the graph of y f(x): a) has a local maximum at x= 2 b) has a local minimum at x 2 c) has an inflection point at x 2 d) has a local maximum at x 4 d) has a local minimum at x 4
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0. Suppose f(x), f '(x) and f are all continuous with the following additional information: f '(3;=6, f'(-z) =0, '(-1)=0 and f"(-z)=0. Furthermoresupposethesignsof '(x) are given in the charts below: > 0 0 o f'(x)<0 I -2 f"(x)>O 0 f"(x)<O 0 f"(").0 tl -2 -1 Given all this information the function y = f(x) has: a) Alocalminimum at x=-2 andinflectionpoints at x=-2 and x=-1 b) Alocalmaximumat x=3 andinflectionpoints at x=-2 c) Alocalminimum at x=-2, alocalmaximumat x=3 andnoinflectionpoints d) A local maximum at x 3 and only one inflection point which is at x = -2 e) A local maximum at x = -2 = -1 1. Suppose f(x) ;3 + (3/2)xt - 6x + 36 is defined only on the dosed interval -4 3 xS 2. Then for f(x) defined on this interval: a) The global maximum of f(x) occurs at x = -4 and the global minimum occurs at x b) The global maximum of f(x) occurs at x 2 c) The global maximum of f(x) occurs at x = -4 d) The global rnaximum of f(x) occurs at x 1 e) The global maximum of f(x) occurs at x 2 2. The cost of selling ducks is given by C(q) 200,000 150q2 while the revenue is R(q) 9000q. Find the quantity q that maximizes profit from selling these ducks.
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This note was uploaded on 11/30/2011 for the course MATH 127 taught by Professor Rudvalis during the Fall '07 term at UMass (Amherst).

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Exam 2 Practice 2 - i . I f f (x) = (U4)x4- + ( 213)x3 (...

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