# Analysis derivative proof

## Homework Statement

Let f : (a, b)--> R be differentiable on (a,b), and assume that f'(x) unequal 1 for all x in (a,b).
Show that there is at most one point c in (a,b) satsifying f(c) = c.

## The Attempt at a Solution

I think that We need to use the mean value theorem for this problem.

This is what I know, but I'm not sure what I should use for my proof:
If we let c be n (a,b)
By definition f'(c)=lim: x-->c (f(x)-f(c)/x-c) assuming that f(x) is differentiable at c.

Also, the mean value theorem states that f[a,b]-->R is continuous on [a.b] and differentiable on (a,b), then there exists a point c in (a,b) so that f'(c)=f(b)-f(a)/b-a

Any help/hints would be great!
The text passage is a homework problem and solution attempt for a proof in calculus. It does not contain any explicit mathematical questions or calculations, but rather a statement of a theorem to prove and an outline of a proof approach.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Analysis derivative proof

## Homework Statement

Let f : (a, b)--> R be differentiable on (a,b), and assume that f'(x) unequal 1 for all x in (a,b).
Show that there is at most one point c in (a,b) satsifying f(c) = c.

## The Attempt at a Solution

I think that We need to use the mean value theorem for this problem.

This is what I know, but I'm not sure what I should use for my proof:
If we let c be n (a,b)
By definition f'(c)=lim: x-->c (f(x)-f(c)/x-c) assuming that f(x) is differentiable at c.

Also, the mean value theorem states that f[a,b]-->R is continuous on [a.b] and differentiable on (a,b), then there exists a point c in (a,b) so that f'(c)=f(b)-f(a)/b-a

Any help/hints would be great!
user
The text passage is a homework problem and solution attempt for a proof in calculus. It does not contain any explicit mathematical questions or calculations, but rather a statement of a theorem to prove and an outline of a proof approach.

TYPE: NO_QUESTION