Convex Function

A convex function is a satisfied if for every pair of points \(x_1 < x_2\), if you were to draw a line through the two points then there exists no value \(x\) (\(x_1 \le x \le x_2\)) such that \(f(x)\) is above the line. This condition implies two important properties of either:

• The convex function has no extrema

• The convex fucntion has a single extrema

• All extremum are global extrema.