$\text { Locate the absolute extrema of the function } f ( x ) = x ^ { 3 } - 12 x \text { on the closed interval }$

Multiple Choice

$\text { Locate the absolute extrema of the function } f ( x ) = x ^ { 3 } - 12 x \text { on the closed interval }$ $[ 0,4 ] .$

A) absolute max: $( 2 , - 16 ) ;$ absolute min: $( 4,16 )$
B) no absolute max; absolute min: $( 4,16 )$
C) absolute max: $( 4,16 ) ;$ absolute min: $( 2 , - 16 )$
D) absolute max: $( 4,16 )$ ; no absolute min
E) no absolute max or min