Question:

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 p

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.

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.