Originally Posted by

**smiler** thanks for your assistance, but no i dont know how to derive that

Did you try ? That's less difficult than it looks like. Starting from

$\displaystyle \left|\frac{\phi(x)-\phi(y)}{x-y}\right|\leq k$ for all $\displaystyle x,y\in A,\, x\neq y$,

if we let $\displaystyle x$ tend to $\displaystyle y$ we get that for all $\displaystyle y \in A$,

$\displaystyle \lim_{x\to y}\left|\frac{\phi(x)-\phi(y)}{x-y}\right| \leq \lim_{x\to y} k$

What is the LHS (think about the definition of the derivative) ? What is the RHS ?

because we havent been shown

That sounds like "I don't have the solution so I can't do it"...

nor do i know what the mean value theorem is.

I can't think of a proof that doesn't use this theorem.