# simple question -- convexity

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• August 8th 2010, 09:40 AM
rainer
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
• August 11th 2010, 11:06 PM
chisigma
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

$\chi$ $\sigma$
• August 14th 2010, 12:06 AM
rainer
So apparently a convex set and a convex function are different things.