what is the average rate of change of the function (f(x)=2x^{2}+8) over the interval (2,6)?\na 2\nb 4\nc…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$, $b = 6$, and $f(x)=2x^{2}+8$.

Step2: Calculate $f(6)$

Substitute $x = 6$ into $f(x)$: $f(6)=2\times6^{2}+8=2\times36 + 8=72 + 8=80$.

Step3: Calculate $f(2)$

Substitute $x = 2$ into $f(x)$: $f(2)=2\times2^{2}+8=2\times4 + 8=8 + 8=16$.

Step4: Calculate average rate of change

$\frac{f(6)-f(2)}{6 - 2}=\frac{80 - 16}{4}=\frac{64}{4}=16$.

Answer:

D. 16