|Dror Bar-Natan: Classes: 2002-03: Math 157 - Analysis I:||(113)||
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We are skipping the appendix on convexity of Spivak's Chapter 11, but it is still worthwhile to take something from it (without proof):
Theorem. The following are equivalent, for a function defined on some interval (assuming is such that these statements make sense):
If any of these statements holds, we say that `` is convex''. There is a similar theorem with all inequalities reversed, and then the name is `` is concave''.