Name: Tammy
Who is asking: Student
Level: Secondary

Question:
suppose that the average rate of change of a function f over the interval from x=3 to x=3+h is given by 5e^h-4cos(2h). what is f'(3)? I would appreciate any help with this question.

Hi Tammy

The rate of change of f is f' so the average rate of change of f from 3 to 3+h is

Thus

Since f is an antiderivative of f',

Thus

Now take the limit of both sides as h approaches 0.

Cheers
Harley