Help w/calculus problem



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].

If anyone here would be kind enough to offer their insights, advice,
guidance--it would be greatly appreciated.


Thanks,
Dean

.



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