Help Intermediate Value Theorem problem

[c299792458]

Homework Statement

I have posted this problem earlier but there was a typo such that the problem didn't make sense... I am still stuck and would appreciate a nudge in the right direction.

I am given that f(x) is continuous on [0,1] and f(0)=f(1)
and I have to show that for any n there exists a point a(n) in [0, 1-(1/n)] s.t. f(a+(1/n))=f(a)


2. Homework Equations
see above


3. The Attempt at a Solution
I have defined a new function, say g(x)= f(a+(1/n))-f(a) and am thinking of using the IVT to prove that there exists a point where g(x)=0 but am not quite sure how.

Thanks!

 

[hunt_mat]

If f(x) is differentiable as well then we could appeal to Rolle's theorem and we would be done as you know what the curve looks like.

 

[c299792458]

Thanks, hunt_mat. But unfortunately f is not necessarily differentiable. I am quite sure that the question is appealing to just continuity.

 

[c299792458]

Hi, the problem is solved. Thanks anyway!