Question

Calculate the average rate of change over the interval [-1,3] for the function:

f(x)= x^2 + 2x - 2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the average rate of change for the function f(x) = x^2 + 2x - 2 over the interval [-1,3], we need to find the difference in the function values at the endpoints of the interval and then divide this by the difference in the x-values.

First, let's find the function values at the two endpoints:
f(-1) = (-1)^2 + 2(-1) - 2 = 1 - 2 - 2 = -3
f(3) = (3)^2 + 2(3) - 2 = 9 + 6 - 2 = 13

Now, let's calculate the average rate of change:
Average rate of change = (f(3) - f(-1)) / (3 - (-1))
= (13 - (-3)) / (3 + 1)
= (13 + 3) / 4
= 16 / 4
= 4

So, the average rate of change of the function f(x) = x^2 + 2x - 2 over the interval [-1,3] is 4.