calculate the average rate of change over the interval [-1,3] for the function show your work in easy steps
f(x) = x^2 + 2x - 2
To calculate the average rate of change over the interval [-1,3] for the function f(x) = x^2 + 2x - 2, follow these steps:
1. Find the value of the function at the end points of the interval:
f(-1) = (-1)^2 + 2(-1) - 2 = 1 - 2 - 2 = -3
f(3) = (3)^2 + 2(3) - 2 = 9 + 6 - 2 = 13
2. Determine the change in the function values over the interval:
Change in f(x) = f(3) - f(-1) = 13 - (-3) = 16
3. Calculate the change in x over the interval:
Change in x = 3 - (-1) = 4
4. Finally, find the average rate of change over the interval:
Average rate of change = Change in f(x) / Change in x
= 16 / 4
= 4
Therefore, the average rate of change over the interval [-1,3] for the function f(x) = x^2 + 2x - 2 is 4.
dont explain the steps just show the steps
1. f(-1) = -3, f(3) = 13
2. Change in f(x) = 13 - (-3) = 16
3. Change in x = 3 - (-1) = 4
4. Average rate of change = Change in f(x) / Change in x = 16 / 4 = 4