- #1

Icebreaker

I need the following proposition in order to prove another theorem, and I can't seen to find it in my textbook. Any hints on how to proceed, or whether it's actually TRUE, would be helpful.

"If f is defined and continuous on some interval I, then there exists subintervals I'=[x-a,x+b], for some real numbers a and b, at every point x in I such that f is monotone on I'."

"If f is defined and continuous on some interval I, then there exists subintervals I'=[x-a,x+b], for some real numbers a and b, at every point x in I such that f is monotone on I'."

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