Determine the Open Intervals on Which the Graph of the Function

Multiple Choice

Determine the open intervals on which the graph of the function
$f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 625 }$ is concave upward or concave downward.

A) concave upward: $\left( - \infty , - \frac { 25 \sqrt { 3 } } { 3 } \right) , \left( \frac { 25 \sqrt { 3 } } { 3 } , \infty \right) ;$ concave downward: $\left( - \frac { 25 \sqrt { 3 } } { 3 } , \frac { 25 \sqrt { 3 } } { 3 } \right)$
B) concave upward: $\left( - \frac { 25 \sqrt { 3 } } { 3 } , \frac { 25 \sqrt { 3 } } { 3 } \right) ;$ concave downward: $\left( - \infty , - \frac { 25 \sqrt { 3 } } { 3 } \right) , \left( \frac { 25 \sqrt { 3 } } { 3 } , \infty \right)$
C) concave upward: $( - \infty , 0 )$ ; concave downward: $( 0 , \infty )$
D) concave upward: $\left( - \frac { 625 } { 3 } , \frac { 625 } { 3 } \right) ;$ concave downward: $\left( - \infty , - \frac { 625 } { 3 } \right) , \left( \frac { 625 } { 3 } , \infty \right)$
E) concave upward: $\left( - \infty , - \frac { 625 } { 3 } \right) , \left( \frac { 625 } { 3 } , \infty \right) ;$ concave downward: $\left( - \frac { 625 } { 3 } , \frac { 625 } { 3 } \right)$