Let f be a twice-differentiable function with derivative given by f'(x) = 4x - 24x.(A) Find the x-coordinate of any possible critical points of f.

Let f be a twice-differentiable function with derivative given by f'(x) = 4x³ - 24x².(A) Find the x-coordinate of any possible critical points of f. Show your work.(B) Find the x-coordinate of any possible inflection points of f. Show your work.(C) Use the Second Derivative Test to determine any relative extrema and inflection points. Justify your answers.(D) If f has only one critical point on the interval [5, 8], what is true about the function f on the interval [5, 8]? Justify your answers.