2001 AB

# 4 the function f is differentiable for all real

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This document was uploaded on 05/03/2012.

Ask a homework question - tutors are online