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→Operations that preserve convexity: [Any mathematicians out there, PLEASE verify this correction!] The statement "-f is concave IFF f is convex" is not universally true - x^3 and -x^3 are both concave - but for x > 0, x^3 is convex while -x^3 is concave, and vice versa for x < 0. If I am wrong here, please correct this and immediately whack me with a wet trout. Tag: Reverted |
m Dating maintenance tags: {{Citation needed}} Tag: Reverted |
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==Operations that preserve convexity==
* <math>-f</math> is concave at a given part of its ___domain if and only if <math>f</math> is convex at that part of its ___domain.{{citation needed|date=February 2023}} <!-- I'm not certain this is right; if it is wrong, please correct it -->
* If <math>r</math> is any real number then <math>r + f</math> is convex if and only if <math>f</math> is convex.
* Nonnegative weighted sums:
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