[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby
\begin{array}{llll}
average\ rate\\
of\ change
\end{array} \\\\
-------------------------------\\\\[/tex]
[tex]\bf h(t)=cot(t)\qquad
\begin{cases}
t_1=\frac{3\pi }{2}\\
t_2=\frac{\pi }{6}
\end{cases}\implies \cfrac{h\left( \frac{\pi }{6} \right)-h\left( \frac{3\pi }{2} \right)}{\frac{\pi }{6}-\frac{3\pi }{2}}
\\\\\\
\cfrac{cot\left( \frac{\pi }{6} \right)-cot\left( \frac{3\pi }{2} \right)}{\frac{\pi }{6}-\frac{3\pi }{2}}\implies \cfrac{\sqrt{3}-0}{\frac{5\pi }{3}}\implies \cfrac{3\sqrt{3}}{5\pi }[/tex]
