I have a function which does not have a closed form . Large numerical effort should be done to evaluate the function for even a single point. How can I examine the convexity of my function over the whole domain of function with minimum computational load?

I have a function which does not have a closed form . Large numerical effort should be done to evaluate the function for even a single point. How can I examine the convexity of my function over the whole domain of function with minimum computational load? some extra assumption is that the function is continuous and almost every where differentiable!