[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}\\\\
-------------------------------\\\\
f(x)= 3x^2+2x+1 \qquad
\begin{cases}
x_1=2\\
x_2=4
\end{cases}\implies \cfrac{f(4)-f(2)}{4-2}
\\\\\\
\cfrac{[3(4)^2+2(4)+1]~~-~~[3(2)^2+2(2)+1]}{2}
\\\\\\
\cfrac{[48+8+1]~~-~~[12+4+1]}{2}\implies \cfrac{57-17}{2}
\\\\\\
\cfrac{60}{2}\implies \cfrac{30}{1}\implies 30[/tex]
