Let f be a twice-differentiable function with derivative given by f('X) = 4x^3-24x^2. Part A: Find the x-coordinate of any possible critical points of f. Show your work. (2 points)
Part B: Find the x-coordinate of any possible inflection points of f. Show your work. (2 points)
Part C: Use the Second Derivative Test to determine any relative extrema and inflection points. Justify your answers. (3 points)
Part D: If has only one critical point on the interval (5,8), what is true about the function of f on the interval [5, 8]? Justify your answers.