Find the Points of Inflection and Discuss the Concavity of the Function

Multiple Choice

Find the points of inflection and discuss the concavity of the function. $f ( x ) = 4 x ^ { 3 } - 5 x ^ { 2 } + 5 x - 7$

A) inflection point at $x = - \frac { 5 } { 12 } ;$ concave upward on $\left( - \infty , - \frac { 5 } { 12 } \right)$ ; concave downward on $\left( - \frac { 5 } { 12 } , \infty \right)$
B) inflection point at $x = \frac { 5 } { 24 }$ ; concare downward on $\left( - \infty , \frac { 5 } { 24 } \right) ;$ concave upward on $\left( \frac { 5 } { 24 } , \infty \right)$
C) inflection point at $x = \frac { 5 } { 12 } ;$ concave downward on $\left( - \infty , \frac { 5 } { 12 } \right)$ ; concave upward on $\left( \frac { 5 } { 12 } , \infty \right)$
D) inflection point at $x = - \frac { 5 } { 12 } ;$ concave downward on $\left( - \infty , - \frac { 5 } { 12 } \right)$ ; concave upward on $\left( - \frac { 5 } { 12 } , \infty \right)$
E) inflection point at $x = \frac { 5 } { 12 }$ ; concave upward on $\left( - \infty , \frac { 5 } { 12 } \right)$ ; concave downward on $\left( \frac { 5 } { 12 } , \infty \right)$