Question

What is the average rate of change for the function f(x) = 3x²- 5 on the interval —3 < x < 1? Write the average rate of change

Answer 1

-6

Step-by-step explanation:

The average rate of change of a function f(x) on an intervale a < x < b is equal to:

`(f(b)-f(a))/(b-a)`

So, to calculate the average rate of change on the interval -3 < x < 1, we first need to calculate f(-3) and f(1) as:

`\begin{gathered} f(x)=3x^2-5 \\ f(-3)=3(-3)^3-5=3(9)-5=22 \\ f(1)=3(1)^2-5=3(1)-5=-2 \end{gathered}`

Therefore, the average rate of change is equal to:

`(f(1)-f(-3))/(1-(-3))=(f(1)+f(-3))/(1+3)=(-2-22)/(4)=(-24)/(4)=-6`

Then, the average rate of change is -6