since many functions, such as f(x)= |x| are convex but not differentiable, a more general definition for convexity is needed.

Geometrically, a function is convex on a region if, given two points on the graph of the function, the straight line joining those points lies entirely above or upon the portion of the graph between those two points. Explain how this translates into the algebraic condition that any two values, x₁, x₂within the domain of convexity, we have

f(ax₁+bx₂) less than or equal to af(x₁)+bf(x₂) for any a,b > 0 satisfying a+b=1