Thread: 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

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

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