Question

question
find the average rate of change of the function (f(x)=-2x^{2}+5) between (x = - 1) and (x = 3).
provide your answer below:

Explanation:

Step1: Find f(-1)

$f(-1)=-2(-1)^2 + 5=-2 + 5=3$

Step2: Find f(3)

$f(3)=-2(3)^2+5=-2\times9 + 5=-18 + 5=-13$

Step3: Calculate average rate of change

The formula for average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here $a=-1$, $b = 3$, so $\frac{f(3)-f(-1)}{3-(-1)}=\frac{-13 - 3}{3+1}=\frac{-16}{4}=-4$

Answer:

-4