1. ## derivatives of functions

Problem 5:[/b]

Suppose that f : [0,1)---IR is continuous on [0,1), differentiable on
(0,00), f(0) = 0, and lim f(x) = 0 as x tends to 00. Prove that there exists a point c in (0,00) such
that f'(c) = 0.

2. ## Re: derivatives of functions

Originally Posted by skybluesea2010
Problem Suppose that f : [0,1)---IR is continuous on [0,1), differentiable on (0,00), f(0) = 0, and lim f(x) = 0 as x tends to 00. Prove that there exists a point c in (0,00) such that f'(c) = 0.
What is IR?

3. ## Re: derivatives of functions

R is just set of real numbers

4. ## Re: derivatives of functions

In these conditions there is either a global maximum or a global minimum so...