[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}\\\\
-------------------------------\\\\
h(x)= 2^x \qquad
\stackrel{2\le x\le 4}{\begin{cases}
x_1=2\\
x_2=4
\end{cases}}\implies \cfrac{h(4)-h(2)}{4-2}\implies \cfrac{2^4-2^2}{2}
\\\\\\
\cfrac{16-4}{2}\implies \cfrac{12}{2}\implies 6[/tex]
