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AP CALCULUS abdominal muscle 2008 SCORING indict (Form B)

inquiry 4

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The features f and g are offered by ( )3 20

4x

f x t dt= + and ( ) ( )sin .g x f x=

(a) discover ( )f x and also ( ).g x (b) compose an equation for the line tangent come the graph that ( )y g x= at .x = (c) Write, yet do not evaluate, an integral expression the represents the maximum value of g on the

interval 0 .x Justify her answer.

(a) ( ) ( )23 4 3f x x = +

( ) ( )

( )2

sin cos

3 4 3sin cos

g x f x x

x x

=

= +

4 : ( )( ) 2 : 2 :

f xg x

(b) ( ) 0,g = ( ) 6g = Tangent line: ( )6y x =

2 : ( ) ( ) 1 : or 1 : tangent line equation

g g

(c) for 0 ,x The maximum worth of g on < >0, is

3 20

4 .t dt+

3 :

( )

( )

1 : sets 0

1 : justifies maximum at 2

1 : integral expression for 2

g x

g

=

126

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