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Math Help - Continuous Functions

  1. #1
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    Continuous Functions








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  2. #2
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    Quote Originally Posted by acevipa View Post








    I'll show you number 1.

    Define the function g(a)=f(a)-f(a+1/2) and note it is continuous. Then, we have g(0) = f(0)-f(1/2) and g(1/2) = f(1/2)-f(1). Depending on the size of f(1/2) relative to f(0)=f(1), we either have g(a) goes from negative to positive or positive to negative. In either case, we have that g(a) = 0 at some point from 0 to 1/2. This shows number 1.
    Last edited by GnomeSain; April 29th 2010 at 03:11 PM.
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