4 the function f is differentiable for all real

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Unformatted text preview: Placement Program and AP are registered trademarks of the College Entrance Examination Board. 6 AP® CALCULUS AB 2001 SCORING GUIDELINES Question 6 1 is on the graph of 4 dy the slope at each point x , y on the graph is given by  y 2 6 2x . dx 1 and evaluate it at the point 3, . 4 dy f (x ) by solving the differential equation  y 2 6 2x with the initial dx 1 f (3)  . 4 The function f is differentiable for all real numbers. The point 3, y  f (x ) , and (a) Find d 2y dx 2 (b) Find y  condition (a) d 2y dx 2 (b) £ ¦ ¦ 2: ¦ ¦ ¦ ¦ ¦ 3:¦ ¤ ¦ ¦ ¦ ¦ ¦ ¦ 1: ¦ ¦ ¥ d 2y dy  2y (6 2x ) 2y 2 2 dx dx 3 = 2y (6 2x )2 2y 2 3, 1 4 0 1 dy  (6 y2 2 x2 4  18 9 y x 2 2  1 8 2x ) dx 1  6x y C 1 4 £ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ 6:¦ ¤ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¥ C C 9 C 13 1 6x d 2y dx 2 < 2 > product rule or chain rule error value at 3, 1 4 1 : separates variables 1 : antiderivative of dy term 1 : antiderivative of dx term 1 : constant of integration 1 : uses initial condition f (3)  1 : solves for y 1 4 Note: max 3/6 [1-1-1-0-0-0] if no 13 constant of integration Note: 0/6 if no separation of variables Copyright © 2001 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 7...
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This document was uploaded on 05/03/2012.

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