(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A function is continuous/differentiable on the interval [0,3]. I have been given that f(0)=1, f(1)=2, f(3)=2.

I need to prove that there exists a c within the interval [0,3] such that f(c) = c.

2. Relevant equations

3. The attempt at a solution

f(1)=f(3)=2. From Rolle's theorem, there exists a c within [1,3] such that f`(c)=0. From this I am able to show that at some point c within [1,3] the function must be constant i.e f(c)=k.

I am not sure how to show that the constant is equal to the point i.e k=c.

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# Rolle's theorem (maybe)

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