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Math Help - Cont. Proof

  1. #1
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    Cont. Proof

    prove if f,g are cont. on  [a,b], if  f(a) < g(a), f(b) > g(b), then there is a c \in [a,b] s.t. f(c) = g(c).

    Ok so I believe I need to prove this using the Intermediate Value Thm. Do I need to apply the IVT to f - g? If that's even a correct approach, how do I begin to do that?
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  2. #2
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    Quote Originally Posted by Math2010 View Post
    prove if f,g are cont. on  [a,b], if  f(a) < g(a), f(b) > g(b), then there is a c \in [a,b] s.t. f(c) = g(c).
    Define h(x)=f(x)-g(x) then h(a)<0~\&~h(b)>0.
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