$\text { For the function } f ( x ) = 4 x ^ { 3 } - 48 x ^ { 2 } + 6 \text { : }$

$\text { For the function } f ( x ) = 4 x ^ { 3 } - 48 x ^ { 2 } + 6 \text { : }$
(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) $x = 0,2$
(b) increasing: $( - \infty , 0 ) \cup ( 2 , \infty )$ ; decreasing: $( 0,2 )$
(c) relative max: $f ( 0 ) = 6$ ; relative min: $f ( 2 ) = - 154$
B)
(a) $x = 0,2$
(b) decreasing: $( - \infty , 0 ) \cup ( 2 , \infty )$ ; increasing: $( 0,2 )$
(c) relative min: $f ( 0 ) = 6$ ; relative $\max : f ( 2 ) = - 154$
C)
(a) $x = 0,2$
(b) increasing: $( - \infty , 0 ) \cup ( 2 , \infty )$ ; decreasing: $( 0,2 )$
(c) relative max: $f ( 0 ) = 6$ ; no relative min.
D)
(a) $x = 0,8$
(b) increasing: $( - \infty , 0 ) \cup ( 8 , \infty )$ ; decreasing: $( 0,8 )$
(c) relative max: $f ( 0 ) = 6$ ; relative min: $f ( 8 ) = - 1018$
E)
(a) $x = 0,8$
(b) decreasing: $( - \infty , 0 ) \cup ( 8 , \infty )$ ; increasing: $( 0,8 )$
(c) relative min: $f ( 0 ) = 6$ ; relative max: $f ( 8 ) = - 1018$