Find the Extrema of the Function on the Given Interval $\sin 4 x , 0 \leq x \leq \frac { \pi } { 2 }$

question 292

Multiple Choice

Find the extrema of the function on the given interval, and say where they occur.
- $\sin 4 x , 0 \leq x \leq \frac { \pi } { 2 }$

• A) local maxima: 1 at \(x = \frac { \pi } { 8 }\) and 0 at \(x = \frac { \pi } { 2 }\);
• local minima: 0 at \(x = 0\) and \(- 1\) at \(x = \frac { 3 \pi } { 8 }\)
• B) local maxima: 1 at \(x = \frac { \pi } { 8 }\) and 0 at \(x = \frac { \pi } { 2 }\);
• local minimum: \(- 1\) at \(x = \frac { 3 \pi } { 8 }\)
• C) local maxima: 1 at \(x = \frac { \pi } { 4 }\) and 0 at \(x = \frac { \pi } { 2 }\);
• local minima: 0 at \(x = 0\) and \(- 1\) at \(x = \frac { 3 \pi } { 8 }\)
• D) local maxima: 1 at \(x = \frac { \pi } { 8 }\) and 0 at \(x = \frac { \pi } { 4 }\);
• local minimum: 0 at \(x = 0\)

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