# Math Help - simple question -- convexity

1. ## simple question -- convexity

What are the mathematical conditions that must be met for a curve to be considered convex?

I would guess that negative slope and a "non-constant" first derivative are essential, but don't know the fancy way of saying this.

Does the bottom left quarter of a circle (from pi to 3pi/2 ) qualify as convex? (If it is plotted up in the first quadrant)

Thanks

2. From...

Convex Function -- from Wolfram MathWorld

... a convex function is a continuous function whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the interval...

Kind regards

$\chi$ $\sigma$

3. So apparently a convex set and a convex function are different things.