Derivative of a Cubic Polynomial Function

Create a calculus-focused diagram that links a cubic polynomial with its derivatives via their zeros. First introduce four user-controlled coefficients to define the cubic function. Then mark the roots associated with the cubic function (show the root locations on the same coordinate setting). Next compute and mark the roots for the first derivative of the cubic. Finally, compute and mark the roots for the second derivative as well. Include concise text indicating which marked points correspond to the function, the first derivative, and the second derivative, so the relationship between these zeros is easy to see.