Proving with mean value theorem

1. Jan 4, 2005

trap

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. Jan 4, 2005

matt grime

Well, what does the mean value theorem say, and what does it imply when you use it as hinted?

3. Jan 4, 2005

Justin Lazear

I'd also keep in mind the definition of a derivative.

--J