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

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    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
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    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.
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