Question

Calculate the average rate of change over the interval [−2,1] given 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 a function over an interval, we use the formula:

Average Rate of Change = [f(b) - f(a)] / (b - a)

In this case, our interval is [-2, 1], so a = -2 and b = 1.

First, we need to find the value of the function f(x) at x = -2 and x = 1:

f(-2) = (-2)^2 + 2(-2) - 2 = 4 - 4 - 2 = -2
f(1) = (1)^2 + 2(1) - 2 = 1 + 2 - 2 = 1

Now, we can plug these values into the formula to find the average rate of change:

Average Rate of Change = [1 - (-2)] / (1 - (-2))
= [1 + 2] / (1 + 2)
= 3 / 3
= 1

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