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…
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 12\nd 16
Answer
Answer:
C. 12
Explanation:
Step1: Recall the 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 the average rate of change
$\frac{f(6)-f(2)}{6 - 2}=\frac{80 - 16}{4}=\frac{64}{4}=16$.