Lost of derivatives or just calcuslus in general

Question

For the function y=4x²

a) Find the average rate of change of "y" with respect to "x" over the interval [5,8]

b) Find the instantaneous rate of change of "y" with respect to "x" at the value x=5

Average rate of change: _____

Instantaneous Rate of Change at x=5: ______

Answer 1

The average rate of the change over the interval [5,8] is (f(8)-f(5))/(8-5)

The rate of change AT POINT is the value of the derivative at this point, f'(5)

f'(x)=8x, so the response is 40.

Average rate of change:42

Instantaneous Rate of Change at x=5:40