CPM Homework Help : CALC Problem 11-131

Multiple Choice: $f(x)$ , shown below, is twice differentiable. Examine the graph and decide which statement below is true.

$f ( 2 ) < f ^ { \prime } ( 2 ) < f ^ { \prime \prime } ( 2 )$
$f ( 2 ) < f ^ { \prime \prime } ( 2 ) < f ^ { \prime } ( 2 )$
$f ^ { \prime } ( 2 ) < f ( 2 ) < f ^ { \prime \prime } ( 2 )$
$f ^ { \prime \prime } ( 2 ) < f ( 2 ) < f ^ { \prime } ( 2 )$
$f ^ { \prime \prime } ( 2 ) < f ^ { \prime } ( 2 ) < f ( 2 )$

Hint:

$f(2) = 0$
$f^\prime(2) =$ slope at $x = 2$ (positive or negative?)
$f^{\prime\prime}(2) =$ concavity at $x = 2$ (up or down?)