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Naddik [55]
3 years ago
13

Need help finding intervals where the function is decreasing.

Mathematics
1 answer:
umka21 [38]3 years ago
8 0

f(x)=-5x-5\sin x\implies f'(x)=-5-5\cos x

f is decreasing on some interval (a,b) if f'(x) for all x\in(a,b). Similarly, f is increasing on (a,b) if f'(x)>0 for all x\in(a,b).

On the domain 0\le x\le2\pi, we have

-5-5\cos x=0\implies\cos x=-1\implies x=\pi

as the only critical point. So we need to check the sign of f' on two intervals, (0,\pi) and (\pi,2\pi).

On (0,\pi), pick any test value. Suppose we take x=\dfrac\pi2. Then f'\left(\dfrac\pi2\right)=-5, so f is decreasing on this interval.

On (\pi,2\pi), you'd find that f'>0, so f is increasing on this interval.

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