Question

Find the average rate of change of g(x) = -1x^3 - 4 from x = -1 to x = 1

Answer 1

Average rate of change = -1

STEP - BY STEP EXPLANATION

What to find?

The average rate of change.

Given:

$g(x)=-1x^3-4$

x₁= -1 and x₂=1

To solve the given problem, we will follow the steps below:

Step 1

Obtain the value of g(x₁) by substituting x₁=-1 into the function given.

$\begin{gathered} g(x_1)=g(-1)=-1(-1)^3-4 \\ \\ =-1(-1)-4 \\ \\ =1-4 \\ =-3 \end{gathered}$

Step 2

Calculate the value of g(x₂) by substituting x₂=1 into the given function.

$\begin{gathered} g(x_2)=g(1)=-1(1)^3-4 \\ \\ =-1-4 \\ =-5 \end{gathered}$

Step 3

Recall the formula for calculating average rate of change.

$\text{Average rate of change=}\frac{g(x_2)-g(x_1)}{x_2-x_1}$

Step 4

Substitute the values and simplify.

$\text{Average rate of change=}\frac{-5-(-3)}{1-(-1)}$$=\frac{-5+3}{2}$$\begin{gathered} =\frac{-2}{2} \\ \\ =-1 \end{gathered}$

Therefore, the average rate of change is -1