# Thread: Show that f is convex on an interval

1. ## Show that f is convex on an interval

Hi there,
this is one of those problems I can't even figure out how to approach. Any idea would be highly appreciated.

Prove that
f is convex on an interval iff for all x and y in the interval,
f(tx + (1 t)y) < tf(x) + (1 t)f(y), for 0 < t < 1

2. Originally Posted by dgmath
Hi there,
this is one of those problems I can't even figure out how to approach. Any idea would be highly appreciated.

Prove that
f is convex on an interval iff for all x and y in the interval,
f(tx + (1 t)y) < tf(x) + (1 t)f(y), for 0 < t < 1

As far as I am concerned this is exactly the definition of (upwards) convexity...which definition do you have?

Tonio

3. Originally Posted by tonio
As far as I am concerned this is exactly the definition of (upwards) convexity...which definition do you have?

Tonio
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I almost guarantee based on dgmath's previous posts that his definition is that $\displaystyle f''(x)>0$. Of course, he/she missing some extra stipulations...differentiability etc.

4. Hi there,
I guess for the same reason, I'm stuck here. what I posted is pretty much all I have, but it IS true that it is a rephrased version of definition of convexity.