A number a is called a fixed point of a function f if f(a)=a. Assuming that f is differentiable and that for every x one has f'(x)does not equal1 prove that f has at most one fixed point.

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- Jan 18th 2010, 06:53 PMamm345Fixed Points- Proof
A number a is called a fixed point of a function f if f(a)=a. Assuming that f is differentiable and that for every x one has f'(x)does not equal1 prove that f has at most one fixed point.

- Jan 18th 2010, 07:01 PMDrexel28
- Jan 18th 2010, 07:23 PMamm345
I think I've got it, can you check this for me?

Suppose f has two fixed point, x1 <x2. Then by MVT we have that

∃y ∈ (x1,x2),__f____(x2) − f(x1)__= f0(y). x2 − x1

Then f0(y)=1 which is a contradiction. - Jan 18th 2010, 07:29 PMDrexel28