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==Examples==
===Functions of one variable===
* The function <math>f(x)=x^2</math> has <math>f''(x)=2>0</math>, so {{mvar|f}} is a convex function. It is also strongly
* The function <math>f(x)=x^4</math> has <math>f''(x)=12x^2\ge 0</math>, so {{mvar|f}} is a convex function. It is strictly convex, even though the second derivative is not strictly positive at all points. It is not strongly convex.
* The [[absolute value]] function <math>f(x)=|x|</math> is convex (as reflected in the [[triangle inequality]]), even though it does not have a derivative at the point ''x'' = 0. It is not strictly convex.
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