Find the interval in which function f(x)=sinx+cosx, 0 x 2 is decreasing:

Question

Find the interval in which function $f (x) = \sin x + \cos x,$ $0 \leq x \leq 2 π$ is decreasing:

Smart Achievers · Accepted Answer

(1)

Ans. $(\frac{π}{4}, \frac{5 π}{4})$

Explanation:

$f (x) = \sin x + \cos x$

$f' (x) = \cos x - \sin x$

Now, $f' (x) = 0$ gives

$\sin x = \cos x,$

which gives that $x = \frac{π}{4}, \frac{5 π}{4}$ as $0 \leq x \leq 2 π .$

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