Re: Help w/calculus problem
- From: matt271829-news@xxxxxxxxxxx
- Date: 16 Jan 2007 19:02:02 -0800
Dean_Travers wrote:
Hello--
I'm currently studying arc length and have reached a problem at the end
of the chapter's exercises which has me stumped; I've tried a couple of
tutors and haven't had any luck. The problem is as follows:
Let y = f(x) be a smooth curve and suppose f'(x) is greater than or
equal to 0 on the closed interval [a, b]. Prove: there are numbers m
and M such that m is less than or equal to f'(x) is less than or equal
to M for all x in [a, b].
I am lousy at these sort of questions, so you'd be better off ignoring
me and listening to someone else. However... m = 0 obviously satisfies
the lower bound. Then, if such M doesn't exist then f'(x) would have to
be somewhere larger than any number, and hence undefined, for some x.
Kind of like y = x^(1/3) over the interval [-1, 1], say (though I'm not
sure that's an entirely legitimate example).
.
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