Question

question 13 · 1 point find the average rate of change of the function f(x)=-2x^{2}-2x - 5 between x=-1 and x = 0. enter an exact answer. provide your answer below: m_{sec}=□

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, $a=-1$, $b = 0$, and $f(x)=-2x^{2}-2x - 5$.

Step2: Calculate $f(-1)$

Substitute $x=-1$ into $f(x)$:
$f(-1)=-2(-1)^{2}-2(-1)-5=-2 + 2-5=-5$.

Step3: Calculate $f(0)$

Substitute $x = 0$ into $f(x)$:
$f(0)=-2(0)^{2}-2(0)-5=-5$.

Step4: Calculate average rate of change

Using the formula $\frac{f(b)-f(a)}{b - a}$, we have $\frac{f(0)-f(-1)}{0-(-1)}=\frac{-5-(-5)}{0 + 1}=\frac{-5 + 5}{1}=0$.

Answer:

$0$