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

Question

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

Quizplus · Accepted Answer

The function $f(x) = \cos(\pi x)$ achieves its maximum value at $x = 0$, where $f(0) = \cos(0) = 1$, and its minimum value at $x = \frac{1}{2}$, where $f\left(\frac{1}{2}\right) = \cos\left(\frac{\pi}{2}\right) = 0$.

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

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