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Homework Help: Proving with mean value theorem

  1. Jan 4, 2005 #1
    Suppose that g(a) = g'(a)=0 and |g''(x)| < M for all x in [a, a+h] (for some positive constant M). Show that |g(a+h)| < Mh^2.
    (Hint: Let k be any number such that 0<= k <= h and apply Mean Value Theorem to g' on [a,a+k].)
  2. jcsd
  3. Jan 4, 2005 #2

    matt grime

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    Well, what does the mean value theorem say, and what does it imply when you use it as hinted?
  4. Jan 4, 2005 #3
    I'd also keep in mind the definition of a derivative.

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