question 8 find the average rate of change of the function f(x)= - 2x² + 3x - 8, from x=-1 to x=3. note, the…

question 8 find the average rate of change of the function f(x)= - 2x² + 3x - 8, from x=-1 to x=3. note, the directions are equivalent to \find the average rate of change over the interval -1,3\. average rate of change = > next question

question 8 find the average rate of change of the function f(x)= - 2x² + 3x - 8, from x=-1 to x=3. note, the directions are equivalent to \find the average rate of change over the interval -1,3\. average rate of change = > next question

Answer

Explanation:

Step1: Recall the formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$, $b = 3$ and $f(x)=-2x^{2}+3x - 8$.

Step2: Calculate $f(-1)$

Substitute $x=-1$ into $f(x)$: $f(-1)=-2(-1)^{2}+3(-1)-8=-2 - 3-8=-13$.

Step3: Calculate $f(3)$

Substitute $x = 3$ into $f(x)$: $f(3)=-2(3)^{2}+3(3)-8=-2\times9 + 9-8=-18+9 - 8=-17$.

Step4: Calculate the average rate of change

$\frac{f(3)-f(-1)}{3-(-1)}=\frac{-17-(-13)}{3 + 1}=\frac{-17 + 13}{4}=\frac{-4}{4}=-1$.

Answer:

$-1$