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Math Help - Help with Proof intro topology

  1. #1
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    Help with Proof intro topology

    Don't really know how to prove this at all, I'm much appreciative of any help, i posted this once before, but really need more of an intro way to solve this proof.

    Let f : [a,b] ⇒ ℝ be a continuous function. Show that there exists a w in [a,b] such that

    a
    ∫ f(t)dt = f(w)(b-a)
    b

    Here is the hint that i need to use to solve this problem:
    f attains a smallest value A and a largest value B. Show that:

    -----------a-----------------------------------------
    A ≤ 1/(b-a)∫ f(t)dt ≤ B
    -----------b-----------------------------------------

    Thank you again for the help!
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