Editing Concave function (section)

==Examples==
* The functions <math>f(x)=-x^2</math> and <math>g(x)=\sqrt{x}</math> are concave on their domains, as their second derivatives <math>f''(x) = -2</math> and <math display="inline">g''(x) =-\frac{1}{4 x^{3/2}}</math> are always negative.
* The [[logarithm]] function <math>f(x) = \log{x}</math> is concave on its domain <math>(0,\infty)</math>, as its derivative <math>\frac{1}{x}</math> is a strictly decreasing function.
* Any [[affine function]] <math>f(x)=ax+b</math> is both concave and convex, but neither strictly-concave nor strictly-convex.
* The [[sine]] function is concave on the interval <math>[0, \pi]</math>.
* The function <math>f(B) = \log |B|</math>, where <math>|B|</math> is the [[determinant]] of a [[nonnegative-definite matrix]] ''B'', is concave.<ref name="Cover 1988">{{cite journal |author-link=Thomas M. Cover |first1=Thomas M. |last1=Cover |first2=J. A. |last2=Thomas |s2cid=5491763 |title=Determinant inequalities via information theory| journal=[[SIAM Journal on Matrix Analysis and Applications]]| year=1988| volume=9|number=3| pages=384&ndash;392| doi=10.1137/0609033}}</ref>