f a function is continuous differentiable and its derivative is monotonic, is the derivative necessarily continuous? Please provide a proof, or if not, give a counterexample.
I cannot provide a proof for this question, but I have tried to find some counterexamples, none of which meet the requirements. For example f（x）=[x] but the function is still differentiable I attempted to use Lagrange's theorem for the proof, but I still think this method is incorrect.he function being continuous does not imply that its derivative is continuous.