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Math Help - continuity problem

  1. #1
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    continuity problem

    What's the idea behind this problem
    Let f and g be continuous functions defined on [0,1]. If f(1/2) = 1, f(3/4) = −6 and g(1/2) = −2, g(3/4) = 3, prove that there exists a c in [0,1] such that (f^2)(c) + 2007f(c) = (g^2)(c) + 2007g(c) ?

    Thanks for any help.
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  2. #2
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    Quote Originally Posted by PvtBillPilgrim View Post
    What's the idea behind this problem
    Let f and g be continuous functions defined on [0,1]. If f(1/2) = 1, f(3/4) = −6 and g(1/2) = −2, g(3/4) = 3, prove that there exists a c in [0,1] such that (f^2)(c) + 2007f(c) = (g^2)(c) + 2007g(c) ?

    Thanks for any help.
    Hint: Define h(x) = f^2(x)+2007f(x) - g^2(x) - 2007g(x). Now show that h has a zero.
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