5. determine the average rate of change of f(x) = x2 + 1 from x = 0 to x = 3.

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 given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$, $b = 3$, and $f(x)=x^{2}+1$.

Step2: Calculate $f(3)$ and $f(0)$

For $x = 3$, $f(3)=3^{2}+1=9 + 1=10$. For $x = 0$, $f(0)=0^{2}+1=1$.

Step3: Substitute into the formula

$\frac{f(3)-f(0)}{3 - 0}=\frac{10 - 1}{3}=\frac{9}{3}=3$.

Answer:

3