This preview shows page 1. Sign up to view the full content.
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 [111000] 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.
 Spring '09
 Calculus

Click to edit the document details