given the function h(x)=x² - 9x + 18, determine the average rate of change of the function over the interval…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = h(x)$ over the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a = 4$, $b = 11$, and $h(x)=x^{2}-9x + 18$.

Step2: Calculate $h(11)$

Substitute $x = 11$ into $h(x)$: $h(11)=11^{2}-9\times11 + 18=121-99 + 18=40$.

Step3: Calculate $h(4)$

Substitute $x = 4$ into $h(x)$: $h(4)=4^{2}-9\times4 + 18=16-36 + 18=-2$.

Step4: Calculate the average rate of change

$\frac{h(11)-h(4)}{11 - 4}=\frac{40-(-2)}{7}=\frac{42}{7}=6$.

Answer:

6