Question

find the average rate of change of $f(x)=-2x^{2}-5x + 7$ over the interval $-5,5$ average rate of change = select choice

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, $a=-5$, $b = 5$, and $f(x)=-2x^{2}-5x + 7$.

Step2: Calculate $f(5)$

Substitute $x = 5$ into $f(x)$:
$f(5)=-2(5)^{2}-5(5)+7=-2\times25-25 + 7=-50-25 + 7=-68$.

Step3: Calculate $f(-5)$

Substitute $x=-5$ into $f(x)$:
$f(-5)=-2(-5)^{2}-5(-5)+7=-2\times25 + 25+7=-50 + 25+7=-18$.

Step4: Calculate the average rate of change

$\frac{f(5)-f(-5)}{5-(-5)}=\frac{-68-(-18)}{5 + 5}=\frac{-68 + 18}{10}=\frac{-50}{10}=-5$.

Answer:

$-5$