(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

prove that if f is continuously differentiable on a closed interval E, then f is Lipschitz continuous on E.

3. The attempt at a solution

so I'm letting E be [a,b]

I'm using the mean value theorem to show secant from a->b = some value, then I'm saying if I subtract epsilon from b over and over, the mean value theorem will still be valid because its continuously differentiable. So in the end I will have secant from any x to y is some value and therefore the entire function is lipschitz continuous.

Seem good?

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

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!

# Homework Help: Function is lipschitz continuous

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