Question

In Exercises $43-50$ , consider the function on the interval $(0,2 \pi) .$ For each function, (a) find the open interval(s) on which the function is increasing or decreasing, (b) apply the First Derivative Test to identify all relative extrema, and (c) use a graphing utility to confirm your results. $$ f(x)=\sin x \cos x+5 $$

          In Exercises $43-50$ , consider the function on the interval $(0,2 \pi) .$ For each function, (a) find the open interval(s) on which the function is increasing or decreasing, (b) apply the First Derivative Test to identify all relative extrema, and (c) use a graphing utility to confirm your results.
$$
f(x)=\sin x \cos x+5
$$

Added by Daniel A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Darshan Maheshwari

01/05/2022

Step 1

Since $ \cos(2x) $ is positive in the intervals $ (0, \frac{\pi}{4}) $ and $ (\frac{3\pi}{4}, \pi) $, the function is increasing in those intervals. The function is decreasing in the intervals $ (\frac{\pi}{4}, \frac{3\pi}{4}) $ and \( (\pi, 2\pi) Show more…

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In Exercises $43-50$ , consider the function on the interval $(0,2 \pi) .$ For each function, (a) find the open interval(s) on which the function is increasing or decreasing, (b) apply the First Derivative Test to identify all relative extrema, and (c) use a graphing utility to confirm your results. $$ f(x)=\sin x \cos x+5 $$