B.5 CONVEX AND CONCAVE FUNCTIONS
Definition: Convex and Concave Function g(x) is convex if for any two values 
and for 
:
(B.28) 
The function is strictly convex if for 
, this expression has strict inequality. Function h(x) is concave if −h(x) is convex. Likewise, the function is strictly concave if −h(x) is strictly convex for 
.
Examples of convex and concave functions are illustrated in Figure B.5. Convex functions are used in Jensen's inequality (see Appendix F).
Figure B.5 Examples of (a) convex g(x) and (b) concave h(x).
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