question given the function h(x)=-x² - x + 3, determine the average rate of change of the function over the…

question given the function h(x)=-x² - x + 3, determine the average rate of change of the function over the interval -4≤x≤6. answer attempt 1 out of 2 submit answer

question given the function h(x)=-x² - x + 3, determine the average rate of change of the function over the interval -4≤x≤6. answer attempt 1 out of 2 submit answer

Answer

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, $a=-4$ and $b = 6$.

Step2: Calculate $h(a)$ and $h(b)$

First, find $h(-4)$: [ \begin{align*} h(-4)&=-(-4)^2-(-4)+3\ &=-16 + 4+3\ &=-9 \end{align*} ] Then, find $h(6)$: [ \begin{align*} h(6)&=-6^2-6 + 3\ &=-36-6 + 3\ &=-39 \end{align*} ]

Step3: Calculate the average rate of change

[ \begin{align*} \frac{h(6)-h(-4)}{6-(-4)}&=\frac{-39-(-9)}{6 + 4}\ &=\frac{-39 + 9}{10}\ &=\frac{-30}{10}\ &=-3 \end{align*} ]

Answer:

$-3$