Calculate the average rate of change over the interval [-1,3] for the function:
f(x)= x^2 + 2x - 2
To find the average rate of change over the interval [-1,3] for the function f(x) = x^2 + 2x - 2, we first need to find the values of f(-1) and f(3).
f(-1) = (-1)^2 + 2(-1) - 2 = 1 - 2 - 2 = -3
f(3) = (3)^2 + 2(3) - 2 = 9 + 6 - 2 = 13
The average rate of change is given by the formula:
Average rate of change = (f(3) - f(-1)) / (3 - (-1))
Substitute the values we found into the formula:
Average rate of change = (13 - (-3)) / (3 - (-1))
Average rate of change = (13 + 3) / 4
Average rate of change = 16 / 4
Average rate of change = 4
Therefore, the average rate of change of the function f(x) = x^2 + 2x - 2 over the interval [-1,3] is 4.