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 of the function f(x) = x^2 + 2x - 2 over the interval [-1,3], we need to find the slope of the secant line passing through the points (-1, f(-1)) and (3, f(3)).

First, let's find the y-coordinates of these points:
f(-1) = (-1)^2 + 2(-1) - 2 = 1 - 2 - 2 = -3
f(3) = (3)^2 + 2(3) - 2 = 9 + 6 - 2 = 13

So the two points are (-1, -3) and (3, 13).

Now, let's calculate the slope of the secant line:
m = (f(3) - f(-1)) / (3 - (-1))
m = (13 - (-3)) / (3 + 1)
m = 16 / 4
m = 4

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