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.(adsbygoogle = window.adsbygoogle || []).push({});

"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'."

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Function Monotone on Some Interval

**Physics Forums | Science Articles, Homework Help, Discussion**