Find the Extrema of the Function on the Given Interval $\sin x + \cos x , 0 \leq x \leq 2 \pi$

question 257

Multiple Choice

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

• A) local maxima: 1 at \(x = 0\) and \(- \sqrt { 2 }\) at \(x = \frac { 5 \pi } { 4 }\);
• local minima: 1 at \(x = 2 \pi\) and \(\sqrt { 2 }\) at \(x = \frac { \pi } { 4 }\)
• B) local maxima: 1 at \(x = 2 \pi\) and \(\sqrt { 2 }\) at \(x = \frac { \pi } { 4 }\);
• local minima: 1 at \(x = 0\) and \(- \sqrt { 2 }\) at \(x = \frac { 5 \pi } { 4 }\)
• C) local maxima: 1 at \(x = 2 \pi\) and \(\sqrt { 2 }\) at \(x = \frac { \pi } { 4 }\);
• local minima: 1 at \(x = 0\) and \(- \sqrt { 2 }\) at \(x = \frac { 7 \pi } { 4 }\)
• D) local maxima: 1 at \(x = 0\) and \(- \sqrt { 2 }\) at \(x = \frac { 7 \pi } { 4 }\);
• local minima: 1 at \(x = 2 \pi\) and \(\sqrt { 2 }\) at \(x = \frac { \pi } { 4 }\)

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Definitions:

Pacinian Corpuscles

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The sense of smell, a complex chemical sensing system that is essential for detecting odors in the environment.

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