question 26 find the average rate of change of the function f(x)= - 2x² - 2x - 1, from x=-3 to x=-2. note…

question 26 find the average rate of change of the function f(x)= - 2x² - 2x - 1, from x=-3 to x=-2. note, the directions are equivalent to \find the average rate of change over the interval -3,-2\. average rate of change = question help: video message instructor submit question

question 26 find the average rate of change of the function f(x)= - 2x² - 2x - 1, from x=-3 to x=-2. note, the directions are equivalent to \find the average rate of change over the interval -3,-2\. average rate of change = question help: video message instructor submit question

Answer

Explanation:

Step1: Recall average - rate - of - change 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, $a=-3$, $b = - 2$, and $f(x)=-2x^{2}-2x - 1$.

Step2: Calculate $f(-3)$

Substitute $x=-3$ into $f(x)$: [ \begin{align*} f(-3)&=-2(-3)^{2}-2(-3)-1\ &=-2\times9 + 6-1\ &=-18 + 6-1\ &=-13 \end{align*} ]

Step3: Calculate $f(-2)$

Substitute $x = - 2$ into $f(x)$: [ \begin{align*} f(-2)&=-2(-2)^{2}-2(-2)-1\ &=-2\times4+4 - 1\ &=-8 + 4-1\ &=-5 \end{align*} ]

Step4: Calculate the average rate of change

[ \begin{align*} \frac{f(-2)-f(-3)}{-2-(-3)}&=\frac{-5-(-13)}{-2 + 3}\ &=\frac{-5 + 13}{1}\ &=8 \end{align*} ]

Answer:

$8$