find the average rate of change of h(x)=x² + 3x + 3 from x = 3 to x = 7. simplify your answer as much as…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = h(x)$ from $x = a$ to $x = b$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a = 3$, $b = 7$, and $h(x)=x^{2}+3x + 3$.

Step2: Calculate $h(7)$

Substitute $x = 7$ into $h(x)$: $h(7)=7^{2}+3\times7 + 3=49+21 + 3=73$.

Step3: Calculate $h(3)$

Substitute $x = 3$ into $h(x)$: $h(3)=3^{2}+3\times3 + 3=9 + 9+3=21$.

Step4: Calculate the average rate of change

$\frac{h(7)-h(3)}{7 - 3}=\frac{73 - 21}{4}=\frac{52}{4}=13$.

Answer:

13