calculate the average rate of change over the interval [-2,1] given the function f(x)=x^2+2x-2
To calculate the average rate of change over the interval [-2,1] for the function f(x) = x^2 + 2x - 2, we first need to find the value of the function at the endpoints of the interval.
f(-2) = (-2)^2 + 2(-2) - 2
f(-2) = 4 - 4 - 2
f(-2) = -2
f(1) = (1)^2 + 2(1) - 2
f(1) = 1 + 2 - 2
f(1) = 1
Next, we calculate the average rate of change by subtracting the value of the function at x = -2 from the value of the function at x = 1, and then dividing by the change in x.
Average rate of change = (f(1) - f(-2)) / (1 - (-2))
Average rate of change = (1 - (-2)) / (1 - (-2))
Average rate of change = (1 + 2) / 3
Average rate of change = 3 / 3
Average rate of change = 1
Therefore, the average rate of change over the interval [-2,1] for the function f(x) = x^2 + 2x - 2 is 1.