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=}(g(x_2)-g(x_1))/(x_2-x_1)`

Step 4

Substitute the values and simplify.

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

Therefore, the average rate of change is -1