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AP® Calculus AB-BC

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Difficult

First And Second Derivative

APCALC-1TBGR8

Given $f( t ) =3t-9,$ if:

$$g( x ) =\int _{ 3 }^{ 2x }{ ( f( t ) ) dt } $$

...which of the following statements must be TRUE?

I. $ g(0) = -\cfrac{27}{2}$
II. $g^\prime(0) = -18$
III. $g^{\prime\prime}(0) = 12$

A

I only

B

II only

C

II and III

D

I, II, and III