Question

question
find the average rate of change of the function
$f(x)$, given below, from $x=-1$ to $x = 1$.
$f(x)=-5x^{3}-4x^{2}-4x - 2$
provide your answer below:

Explanation:

Step1: Calculate f(-1)

$f(-1)=-5(-1)^3 - 4(-1)^2 - 4(-1)-2=5 - 4 + 4 - 2=3$

Step2: Calculate f(1)

$f(1)=-5(1)^3 - 4(1)^2 - 4(1)-2=-5 - 4 - 4 - 2=-15$

Step3: Use average rate - of - change formula

The average rate of change formula is $\frac{f(b)-f(a)}{b - a}$, where $a=-1$, $b = 1$. So $\frac{f(1)-f(-1)}{1-(-1)}=\frac{-15 - 3}{2}=\frac{-18}{2}=-3$

Answer:

-3