Concave and Convex Function

Overview of Concave and Convex Function

Consider a function y = f(x), which is assumed to be continuous on the interval [a, b]. The function y = f(x) is called convex downward (or concave upward) if for any two points and in [a, b], the following inequality holds -

If this inequality is strict for any, Ɛ [a, b], such that ≠ , then, the function f(x) is called strictly convex downward on the interval [a, b].

Comparison between Concave and Convex Function

Similarly, we define a concave function. A function f(x) is called convex upward (or concave downward) if for any two points and in the interval [a, b], the following inequality is valid -

If this inequality is strict for any, Ɛ [a, b], such that ≠ , then, the function f(x) is called strictly convex upward on the interval [a, b].