Show that f has neither a relative maximum nor a relative

Question

Question: Consider the functions f(x) = x³ , g(x) = x⁴ , and h(x) = x⁴.

A. Show that x = 0 is a critical number of each of the functions f, t, and h.

B. Show that the second derivative of each of the functions f, t, and h equals zero at x = 0.

C. Show that f has neither a relative maximum nor a relative minimum at x = 0, that t has a relative minimum at x = 0, and that h has a relative maximum at x = 0.