Question

what is the average rate of change of the function f(x)= - 5x^2 + 7x on the interval -1,3? the average rate of change is

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$, $b = 3$, and $f(x)=-5x^{2}+7x$.

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

First, find $f(-1)$:
$f(-1)=-5\times(-1)^{2}+7\times(-1)=-5 - 7=-12$.
Then, find $f(3)$:
$f(3)=-5\times3^{2}+7\times3=-5\times9 + 21=-45+21=-24$.

Step3: Calculate the average rate of change

Substitute $f(-1)$ and $f(3)$ into the formula $\frac{f(b)-f(a)}{b - a}$:
$\frac{f(3)-f(-1)}{3-(-1)}=\frac{-24-(-12)}{3 + 1}=\frac{-24 + 12}{4}=\frac{-12}{4}=-3$.

Answer:

$-3$