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

question 22

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 \(x = \frac { 1 } { 3 }\).

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