Determine the Critical Points of the Given Function and Classify $f ( x ) = 3 x ^ { 4 } - 8 x ^ { 3 } + 6 x ^ { 2 } + 3$

Multiple Choice

Determine the critical points of the given function and classify each critical point as a relative maximum, a relative minimum, or neither. $f ( x ) = 3 x ^ { 4 } - 8 x ^ { 3 } + 6 x ^ { 2 } + 3$

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