Identify the open intervals on which the function is Increasing or decreasing. (Enter your answers using interval notation.)

Increasing
decreasing

Question

Identify the open intervals on which the function is Increasing or decreasing. (Enter your answers using interval notation.) \[ f(x)=\sin (x)-5 \quad 0

UpStudy AI · Accepted Answer

We begin by finding the derivative of the function
$$
f(x)=\sin(x)-5.
$$
Taking the derivative with respect to $$x$$, we have
$$
f'(x)=\cos(x).
$$

To determine where $$f$$ is increasing or decreasing on $$00$$, i.e., when
   $$
   \cos(x)>0.
   $$
2. $$f$$ is decreasing when $$f'(x)<0$$, i.e., when
   $$
   \cos(x)<0.
   $$

Recall that on the interval $$00$$ for $$0The function $$ f(x) = \sin(x) - 5 $$ is increasing on the intervals $$ (0, \frac{\pi}{2}) $$ and $$ (\frac{3\pi}{2}, 2\pi) $$, and decreasing on the interval $$ (\frac{\pi}{2}, \frac{3\pi}{2}) $$.

Identify the open intervals on which the function is Increasing or decreasing. (Enter your answers using interval notation.)

Increasing
decreasing

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Identify the open intervals on which the function is Increasing or decreasing. (Enter your answers using interval notation.) Increasing decreasing

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