Find the intervals in which the function f given by f(x) = sin x … - Vidyadip

Question

Find the intervals in which the function f given by
f(x) = sin x + cos x, 0 < x < 2 $\pi$.
is strictly increasing or strictly decreasing.

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Answer

f′(x) = cos x – sin x
(x) = o
$\therefore$ Intervals are $\Bigg(0,\frac{\pi}{4}\Bigg),\Bigg(\frac{\pi}{4},\frac{5\pi}{4}\Bigg),\Bigg(\frac{5\pi}{4}2\pi\Bigg).$
Getting f (x) strictly increasing in $\Bigg(0,\frac{\pi}{4}\Bigg)\text{U}\Bigg(\frac{5\pi}{4}2\pi\Bigg).$
and strictly decreasing in $\Bigg(\frac{\pi}{4},\frac{5\pi}{4}\Bigg).$

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