Describe how to determine the average rate of change between x=3 and x=5 for the function f(x) 3x^3+2 Include the average rate of change in your answer.

Question

asked Apr 17, 2023 7.7k views

1 Answer

Saral Karki · Answer 1 · 2023-04-22T08:11:13+0000

Given the function:

$f\mleft(x\mright)=3x^3+2$

You can use the following formula to find the Average Rate of Change:

$Average\text{ }Rate\text{ }of\text{ }Change=(f(b)-f(a))/(b-a)$

Where the following are two points on the function:

$\begin{gathered} (a,f(a)) \\ \\ (b,f(b)) \end{gathered}$

1. You know that you must determine the Average Rate of Change between:

$x=3\text{ and }x=5$

Then, you can set up that:

$\begin{gathered} a=3 \\ b=5 \end{gathered}$

2. In order to find the corresponding value for:

$\begin{gathered} f(a)=f(3) \\ f(b)=f(5) \end{gathered}$

You can follow these steps:

- Substitute the value of "a" into the function and evaluate:

- Substitute the value of "b" into the function and then evaluate:

3. Knowing all the values, you can substitute into the formula for calculating the Average Rate of Change and evaluate:

$Average\text{ }Rate\text{ }of\text{ }Change=(377-83)/(5-3)=(294)/(2)=147$

Hence, the answer is:

You can determine the average rate of change by finding the corresponding output values (y-values) for:

$x=3\text{ and }x=5$

After finding those values, you can substitute them into the formula for calculating the Average Rate of Change, and then evaluate. It is:

$Average\text{ }Rate\text{ }of\text{ }Change=147$