Given:
[tex]f(x)=2x^2+8[/tex][tex][2,6][/tex]To determine the average rate of change, we use the formula:
[tex]A(x)=\frac{f(b)-f(a)}{b-a}[/tex]where:
[a,b] = interval
A(x)= average rate of change
Based on the given formula, we let a=2 and b=6. Hence,
[tex]\begin{gathered} A(x)=\frac{f(b)-f(a)}{b-a} \\ A(x)=\frac{f(6)-f(2)}{6-2} \end{gathered}[/tex]We plug in x=2 into f(x)=2x^2+8:
[tex]\begin{gathered} f(x)=2x^{2}+8 \\ f(2)=2(2)^2+8 \\ Simplify \\ f(2)=16 \end{gathered}[/tex]We plug in x=6 into f(x)=2x^2+8:
[tex]\begin{gathered} f(x)=2x^{2}+8 \\ f(6)=2(6)^2+8 \\ f(6)=80 \end{gathered}[/tex]So,
[tex]\begin{gathered} A(x)=\frac{f(6)-f(2)}{6-2} \\ A(x)=\frac{80-16}{6-2} \\ Simplify \\ A(x)=16 \end{gathered}[/tex]Therefore, the average rate of change is 16.
