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

Multiple Choice

$\text { Locate the absolute extrema of the function } f ( x ) = \sin \pi x \text { on the closed interval }$ $\left[ 0 , \frac { 1 } { 3 } \right]$

A) The absolute minimum is 0 , and it occurs at the left endpoint $x = 0$ . The absolute maximum is $\frac { \sqrt { 3 } } { 2 }$ , and it occurs at the right endpoint $x = \frac { 1 } { 3 }$ .
B) The absolute minimum is 0 , and it occurs at the right endpoint $x = \frac { 1 } { 3 }$ .
The absolute maximum is $\frac { 1 } { 2 }$ , and it occurs at the left endpoint $x = 0$ .
C) The absolute minimum is 0 , and it occurs at the left endpoint $x = 0$ . The absolute maximum is $\frac { 1 } { 2 }$ , and it occurs at the right endpoint $x = \frac { 1 } { 3 }$ .
D) The absolute minimum is 0 , and it occurs at the right endpoint $x = \frac { 1 } { 3 }$ .
The absolute maximum is $\frac { \sqrt { 2 } } { 2 }$ and it occurs at the left endpoint $x = 0$ .
E) The absolute minimum is 0 , and it occurs at the left endpoint $x = 0$ .
The absolute maximum is $\frac { \sqrt { 2 } } { 2 }$ , and it occurs at the right endpoint $x = \frac { 1 } { 3 }$ .