# Convex Function

1. Nov 16, 2008

### ahamdiheme

How do i go about showing that if f(x)=$$\left\|$$x$$\left\|$$ then f(x) is a convex function.

I'm thinking in the direction of the triangle inequality but don't know how to go about it. Any clues? thanks

2. Nov 16, 2008

### tim_lou

it just comes straight from definition of convex function

$$|tx+(1-t)y|\leq |tx| + |(1-t)y|$$

3. Nov 16, 2008

### ahamdiheme

that is it, Thanks a lot!

Last edited: Nov 16, 2008