Proving f(x) Continuity with IVT on [0,1]

[c299792458]

Homework Statement

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 [1, 1-(1/n)] s.t. f(a+(1/n))=f(a)

Homework Equations

see above

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 in advance for any help!

 

[LCKurtz]

I don't think your problem is stated correctly, whatever it is. The first problem is the interval you give [1, 1-1/n] is not in the standard form [u,v] with u ≤ v. But if you meant a is in [1-1/n, 1], that doesn't make any sense in your problem either because then a + 1/n > 1 which is outside the domain of the function.

The first step in analyzing a problem is to understand the statement of the problem which, apparently, you don't.

 

[c299792458]

LCKurtz, I am sorry about the typo, it is supposed to be [0,1-1/n]

 

[c299792458]

Hi, I have solved it, thanks anyway.