Reference no: EM131602446

Question: Sometimes, odd behavior can be hidden beneath the surface of a rather normal-looking function. Consider the following function:

(a) Sketch a graph of this function. Does it have any vertical segments or corners? Is it differentiable everywhere? If so, sketch the derivative f' of this function.

(b) Is the derivative function, f'(x), differentiable everywhere? If not, at what point(s) is it not differentiable? Draw the second derivative of f(x) wherever it exists. Is the second derivative function, f"(x), differentiable? Continuous?