QuestionFind the average rate of change of $h(t)=\cot t$ over the intervals: a. $\left[\frac{3 \pi}{4}, \frac{5 \pi}{4}\right]$ b. $\left[\frac{5 \pi}{6}, \frac{3 \pi}{2}\right]$

Studdy Solution
Substitute the values of $h\left(\frac{3 \pi}{2}\right)$ and $h\left(\frac{5 \pi}{6}\right)$ into the formula.
$$Average\, rate\, of\, change = \frac{0 - (-\sqrt{3})}{\frac{3 \pi}{2} - \frac{5 \pi}{6}} = \frac{\sqrt{3}}{\frac{\pi}{6}} =6\sqrt{3}$$The average rate of change of the function $h(t)=\cot t$ over the interval $\left[\frac{3 \pi}{4}, \frac{5 \pi}{4}\right]$ is $0$ and over the interval $\left[\frac{5 \pi}{6}, \frac{3 \pi}{2}\right]$ is $6\sqrt{3}$.