Find any and all points inside the interval (0,3) where the instantaneous rate of change of f equals the average rate of change of f over the interval [0,3], for the equation
f(x) = 4x^2 - x^3
The Attempt at a Solution
Not really sure how to do this. How do I find the average rate of change over that interval? I was thinking take the derivative:
f'(x) = 8x - 3x^2
plugging in 0 and 3 to get f'(0) = 0, and f'(3) = -3. So the average rate of change would be
And then saying
-1.5 = = 8x - 3x^2? I don't know, gah. How do I solve this problem?