Determine the Critical Points of the Given Function and Classify $f ( x ) = 6 x ^ { 4 } - 48 x ^ { 3 } + 108 x ^ { 2 } + 4$

Multiple Choice

Determine the critical points of the given function and classify each critical point as a relative maximum, a relative minimum, or neither. $f ( x ) = 6 x ^ { 4 } - 48 x ^ { 3 } + 108 x ^ { 2 } + 4$

A) (0, 4) relative minimum; (3, 166) neither
B) (0, 2) neither; (1, 3) relative minimum
C) (0, 2) relative minimum; (1, 4) neither
D) (0, 2) relative minimum; (1, 3) relative maximum