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Unformatted text preview: g ( −1) , g ′( −1) , and g ′′( −1) , find the
value or state that it does not exist.
(b) For the function g defined in part (a), find the
xcoordinate of each point of inflection of the graph
of g on the open interval − 4 < x < 3. Explain
your reasoning.
(c) Let h be the function given by h( x ) = 3 ∫ x f ( t ) dt. Find all values of x in the closed interval − 4 ≤ x ≤ 3 for which h( x ) = 0.
(d) For the function h defined in part (c), find all intervals on which h is decreasing. Explain your
reasoning. (a) g ( −1) = −1 1 15 ∫− 4 f ( t ) dt = − 2 ( 3)( 5) = − 2 g ′( −1) = f ( −1) = −2
g ′′( −1) does not exist because f is not differentiable
at x = −1. ⎧ 1 : g ( −1)
⎪
3 : ⎨ 1 : g ′( −1)
⎪ 1 : g ′′( −1)
⎩ (b) x =1
g ′ = f changes from increasing to decreasing
at x = 1. ⎧ 1 : x = 1 (only)
2: ⎨
⎩ 1 : reason (c) x = −1, 1, 3 2 : correct values
−1 each missing or extra value (d) h is decreasing on [ 0, 2]
h′ = − f < 0 when f > 0 ⎧ 1 : interval
2: ⎨
⎩ 1 : reason Copyright © 2005 by College Board. All rights reserved.
Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 5 AP® CALCULUS AB
2005 SCORING GUIDELINES (Form B)
Question 5 Consider the curve given by y 2 = 2 + xy.
(a) Show that dy
y
=
.
dx 2 y − x (b) Find all points ( x, y ) on the curve where the line tangent to the curve has slope 1
.
2 (c) Show that there are no points ( x, y ) on the curve where the line tangent to the curve is horizontal.
(d) Let x and y be functions of time t that are related by the equation y 2 = 2 + xy. At time t = 5, the
dy
dx
= 6. Find the value of
at time t = 5.
value of y is 3 and
dt
dt (a) (b) 2 y y′ = y + x y′
( 2 y − x ) y′ = y
y
y′ =
2y − x ⎧ 1 : implicit differentiation
2: ⎨...
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This note was uploaded on 10/01/2009 for the course OC 9876 taught by Professor Dq during the Spring '09 term at UC Merced.
 Spring '09
 Dq

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