example of strictly concave function
A function is called strictly concave if. for any t in (0,1) and x â  y. For a function f: R â R, this definition merely states that for every z between x and y, the point (z, f (z)) on the graph of f is above the straight line joining the points (x, f (x)) and (y, f (y)). Any affine function is both (non-strictly) concave and convex. 2  The sine function is concave on the interval. 3  The function, where is the determinant of a nonnegative-definite matrix B, is concave. 4  Practical example: rays bending in computation of radiowave attenuation in the atmosphere.
Note that just monotonic transformation of a concave function isnot necessarily concave: consider, for example f (x) = x and g (z) = z 3 .Thus the concavity of a function is not ordinal, it is cardinal property.Economic ExampleSuppose production function f (x) is concave and the cost function c (x) is convex.ote that just monotonic transformation of a concave function isnot necessarily concave: consider, for example f (x) = x and g (z) = z 3 .Thus the concavity of a function is not ordinal, it is cardinal property.Economic ExampleSuppose production function f (x) is concave and the cost function c (x) is convex.