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AP® Calculus AB-BC

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Difficult

Decreasing And Concave Up

APCALC-1KBDEY

Let $f$ be a continuous, differentiable function.

If $f^{ \prime }( x ) =x(x-2){ ( x+3 ) }^{ 2 }$, for what values of $x$ will $f(x)$ be decreasing and concave up?

A

$( \sqrt{ ( 3/2 )} ,2 ) $

B

$( \sqrt{ ( 3/2 )} ,\infty ) $

C

$( -3,-\sqrt{ ( 3/2 )} )\cup (1,\infty ) $

D

$( -3,-\sqrt{ ( 3/2 )} ) $