Prove this (periodic function)

  • Thread starter sayan2009
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  • #1
please prove this (periodic function)

Homework Statement

if f is periodic continuous function with period 1 then show there exists x such that f(x+pi)=f(x)

Homework Equations

The Attempt at a Solution

i am trying in this way,considering interval [pi,pi+1],and taking g(x)=f(x+pi)-f(x).and trying to use intermediate value theorem...but stuck on that
  • #2

Sine and cosine are cyclic functions...
  • #3

r u tryin to use Fourier expansion
  • #4

sayan2009, I like your function g(x), and I like that you are using the IVT, but your interval doesn't work. You need numbers a and b where g(a) will be positive and g(b) will be negative (or vice versa). I bet you will have good luck if you first consider the fact that f must attain its maximum and minimum values.

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