The function f has a local minimum at x of f has a

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Unformatted text preview: nce Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 5 AP® CALCULUS AB 2001 SCORING GUIDELINES Question 5 A cubic polynomial function f is defined by f (x )  4x 3 ax 2 bx k where a, b, and k are constants. The function f has a local minimum at x  of f has a point of inflection at x  1 , and the graph 2. (a) Find the values of a and b. 1 ¨0 f (x )dx (b) If = 32, what is the value of k ? (a) f a(x )  12x 2 f aa(x )  24x £ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ 5:¦ ¤ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¥ b 2a f a( 1)  12 f aa( 2)  2ax b0 2a 48 2a  0 1 : f a(x ) 1 : f aa(x ) 1 : f a( 1)  0 1 : f aa( 2)  0 1 : a, b a  24 b (b) 1 ¨0 12 4x 3  x4 27 2a  36 24x 2 8x 3 36x 18x 2 £ 2 : antidifferentiation ¦ ¦ ¦ ¦ < 1 > each error ¦ 4:¦ ¤ ¦ 1 : expression in k ¦ ¦ ¦ 1:k ¦ ¦ ¥ k dx kx x 1 x 0  27 k k  32 k5 Copyright © 2001 by College Entrance Examination Board. All rights reserved. Advanced...
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This document was uploaded on 05/03/2012.

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