$\frac{f(t)-f(s)}{t-s}\le \frac{f(u)-f(s)}{u-s}\le \frac{f(u)-f(t)}{u-t}$ for convex $f$

If $f$ is convex in $(a,b)$ and if , then

$$\frac{f(t)-f(s)}{t-s}\le \frac{f(u)-f(s)}{u-s}\le \frac{f(u)-f(t)}{u-t}.$$ (1)

Title	$\frac{f(t)-f(s)}{t-s}\le \frac{f(u)-f(s)}{u-s}\le \frac{f(u)-f(t)}{u-t}$ for convex $f$
Canonical name	fracftfstsleqfracfufsusleqfracfuftutForConvexF
Date of creation	2013-03-22 18:25:32
Last modified on	2013-03-22 18:25:32
Owner	yesitis (13730)
Last modified by	yesitis (13730)
Numerical id	4
Author	yesitis (13730)
Entry type	Theorem
Classification	msc 26A51