find the average rate of change for f(x) = x² + 7x + 10 from x = 0 to x = 2.\na 5\nb 7\nc 9\nd 11

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$, $b = 2$, and $f(x)=x^{2}+7x + 10$.

Step2: Calculate $f(2)$

Substitute $x = 2$ into $f(x)$: $f(2)=2^{2}+7\times2 + 10=4 + 14+10=28$.

Step3: Calculate $f(0)$

Substitute $x = 0$ into $f(x)$: $f(0)=0^{2}+7\times0 + 10=10$.

Step4: Calculate the average rate of change

$\frac{f(2)-f(0)}{2 - 0}=\frac{28 - 10}{2}=\frac{18}{2}=9$.

Answer:

C. 9