?

Free Version
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

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