Find All Relative Extrema of the Function $f ( x ) = - 4 x ^ { 2 } - 32 x - 62$

Multiple Choice

Find all relative extrema of the function $f ( x ) = - 4 x ^ { 2 } - 32 x - 62$ . Use the Second Derivative Test where applicable.

A) relative $\max : f ( 0 ) = - 62$ ; no relative $\min$
B) no relative max; no relative $\min$
C) relative min: $f ( - 4 ) = 2$ ; relative $\max : f ( 0 ) = - 62$
D) relative min: $f ( - 4 ) = 2$ ; no relative $\max$ .
E) relative min: $f ( - 4 ) = 2$ ; relative $\max : f ( 0 ) = - 62$ .