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. $g^{\prime\prime}(0) = 12$