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Thread: simple question -- convexity

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    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)

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    MHF Contributor chisigma's Avatar
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    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

    $\displaystyle \chi$ $\displaystyle \sigma$
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    So apparently a convex set and a convex function are different things.
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