$\text { Locate the absolute extrema of the function } f ( x ) = \cos ( \pi x ) \text { on the closed interval }$

Multiple Choice

$\text { Locate the absolute extrema of the function } f ( x ) = \cos ( \pi x ) \text { on the closed interval }$ $\left[ 0 , \frac { 1 } { 2 } \right]$

A) absolute max: $( 0,1 ) ;$ absolute min: $\left( \left( \frac { 1 } { 2 } \right) , \cos \left( \frac { \pi } { 2 } \right) \right)$
B) absolute max: $\left( \left( \frac { 1 } { 2 } \right) , \cos \left( \frac { \pi } { 2 } \right) \right) ;$ absolute min: $( 0,1 )$
C) absolute max: $\left( \left( \frac { 1 } { 2 } \right) , \cos \left( \frac { \pi } { 2 } \right) \right) ;$ no absolute min
D) no absolute max; absolute min: $( 0,1 )$
E) absolute max: $( 0,1 )$ ; no absolute min