# Function is lipschitz continuous

CarmineCortez

## Homework Statement

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

## 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?