Determine the Relative Extrema of the Function $e ^ { 5 x } \cos x$

question 28

Multiple Choice

Determine the relative extrema of the function $e ^ { 5 x } \cos x$ on the interval $( 0,2 \pi )$ .

• A)relative minimum: \(\left( - \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 25 \pi } { 4 } } , \frac { 5 \pi } { 4 } \right)\) relative maximum: \(\left( \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 5 \pi } { 4 } } , \frac { \pi } { 4 } \right)\)
• B)relative minimum: \(\left( \frac { \pi } { 4 } , - \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 5 \pi } { 4 } } \right)\) relative maximum: \(\left( \frac { 5 \pi } { 4 } , \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 25 \pi } { 4 } } \right)\)
• C)relative minimum: \(\left( \frac { 5 \pi } { 4 } , - \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 25 \pi } { 4 } } \right)\) relative maximum: \(\left( \frac { \pi } { 4 } , \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 5 \pi } { 4 } } \right)\)
• D)relative minimum: \(\left( \frac { 5 \pi } { 4 } , \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 5 \pi } { 4 } } \right)\) relative maximum: \(\left( \frac { \pi } { 4 } , - \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 25 \pi } { 4 } } \right)\)
• E)relative minimum: \(\left( \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 5 \pi } { 4 } } , \frac { 5 \pi } { 4 } \right)\) relative maximum: \(\left( - \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 25 \pi } { 4 } } , \frac { \pi } { 4 } \right)\)

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