True or false... please explain why if false

Let the function f be differentiable on an interval I containing c. If f has a maximum value at x = c, then f has a minimum value at x = c.

A cubic function defined by f(x)= ax^3+bx^2+cx+d where a does not equal 0 will always have exactly three critical numbers

Respuesta :

As this is a trinomial function I believe the answer is true due to the fact that a trinomial curve consists of three parabolic curves in which each has its own respective minimum or maximum value i.e. critical number.