Within (0, π), on which interval is f(x) = sin x + cos x strictly increasing?

Increasing & Decreasing Functions · Question 62 of 74

Question 62

HardOriginal question

Within $(0, \pi)$ , on which interval is $f(x) = \sin x + \cos x$ strictly increasing?

(\frac{\pi}{4}, \pi)

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(0, \frac{\pi}{4})

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(0, \frac{\pi}{2})

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(\frac{\pi}{2}, \pi)

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Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$f'(x) = \cos x - \sin x$ , which is 0 where $\tan x = 1$ : $x = \frac{\pi}{4}$ .
For $0 < x < \frac{\pi}{4}$ , $\cos x > \sin x$ , so $f' > 0$ ; after $\frac{\pi}{4}$ , $f' < 0$ .

Worth noting

$\left(0, \frac{\pi}{2}\right)$ runs past the peak at $\frac{\pi}{4}$ , after which $f$ falls.

Ten questions from Increasing & Decreasing Functions, at your own pace.

Ten questions from Increasing & Decreasing Functions, at your own pace.