Question

Find the average rate of change of f(x) = -2x^2 + 3x^2 from x= -3 to x= 1.
Simplify your answer as much as possible.

Answer 1

The average rate of change of a function over an interval is given by the difference in the function values at the endpoints of the interval divided by the difference in the x-values at the endpoints.

In this case, we have f(x) = -2x^2 + 3x, and we want to find the average rate of change from x = -3 to x = 1.

f(-3) = -2(-3)^2 + 3(-3) = -18 - 9 = -27
f(1) = -2(1)^2 + 3(1) = -2 + 3 = 1

The average rate of change is then given by:

(1 - (-27)) / (1 - (-3)) = 28 / 4 = 7

Therefore, the average rate of change of f(x) = -2x^2 + 3x from x = -3 to x = 1 is 7.