# Math Help - Function is not continuously differentiable, can I show it is concave?

1. ## Function is not continuously differentiable, can I show it is concave?

Dear All.
I am trying to prove structural properties of a function which is not differentiable at a single interior point. Is there any way to prove that the function is concave even though it is not continuously differentiable everywhere?
Thanks for your help

2. That surely depends upon the function and how you prove it is concave. The definition of "concave function" says nothing about differentiability. For example, the function f(x)= 1- |x| is concave but not differentiable at x= 0.