Question

question
find the average rate of change of the function $f(x)$, given below, from $x=-2$ to $x = 2$.
$f(x)=-4x^{2}-x - 3$
provide your answer below:

Explanation:

Step1: Find f(-2)

Substitute x = - 2 into f(x):
$f(-2)=-4\times(-2)^{2}-(-2)-3=-4\times4 + 2-3=-16 + 2-3=-17$

Step2: Find f(2)

Substitute x = 2 into f(x):
$f(2)=-4\times2^{2}-2-3=-4\times4-2 - 3=-16-2-3=-21$

Step3: Calculate average rate of change

The formula for the average rate of change of a function from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$, $b = 2$.
$\frac{f(2)-f(-2)}{2-(-2)}=\frac{-21-(-17)}{2 + 2}=\frac{-21 + 17}{4}=\frac{-4}{4}=-1$

Answer:

-9