Use the Second Derivative Test to Find the Relative Maxima $f ( x ) = 4 x ^ { 3 } + 12 x ^ { 2 } - 36 x + 1$

Multiple Choice

Use the second derivative test to find the relative maxima and minima of the function $f ( x ) = 4 x ^ { 3 } + 12 x ^ { 2 } - 36 x + 1$ .

A) Relative maximum at (1, 109) ; relative minimum at (-3, -19)
B) Relative maximum at (-3, -19) ; relative minimum at (-1, 45)
C) Relative maximum at (-3, -18) ; relative minimum at (1, 109)
D) Relative maximum at (-3, 109) ; relative minimum at (1, -19)