For the Function $f ( x ) = 2 x ^ { 3 } - 12 x ^ { 2 } + 2$

For the function $f ( x ) = 2 x ^ { 3 } - 12 x ^ { 2 } + 2$ : (a) Find the critical numbers of f (if any) ;
(b) Find the open intervals where the function is increasing or decreasing; and
(c) Apply the First Derivative Test to identify all relative extrema.
Then use a graphing utility to confirm your results.

A) (a) $x = 0,4$
(b) increasing: $( - \infty , 0 ) \cup ( 4 , \infty )$ ; decreasing: $( 0,4 )$
(c) relative max: $f ( 0 ) = 2$ ; relative min: $f ( 4 ) = - 62$
B) (a) $x = 0,4$
(b) decreasing: $( - \infty , 0 ) \cup ( 4 , \infty )$ ; increasing: $( 0,4 )$
(c) relative min: $f ( 0 ) = 2$ ; relative max: $f ( 4 ) = - 62$
C) (a) $x = 0,1$
(b) increasing: $( - \infty , 0 ) \cup ( 1 , \infty )$ ; decreasing: $( 0,1 )$
(c) relative max: $f ( 0 ) = 2$ ; relative min: $f ( 1 ) = - 8$
D) (a) $x = 0,1$
(b) decreasing: $( - \infty , 0 ) \cup ( 1 , \infty )$ ; increasing: $( 0,1 )$
(c) relative min: $f ( 0 ) = 2$ ; relative max: $f ( 1 ) = - 8$
E) (a) $x = 0,1$
(b) increasing: $( - \infty , 0 ) \cup ( 1 , \infty )$ ; decreasing: $( 0,1 )$
(c) relative $\max : f ( 0 ) = 2$ ; no relative min.