Question: A cubic function is a polynomial of degree 3; that is, it has the form f sxd ax3 1 bx2 1 cx 1 d,

A cubic function is a polynomial of degree 3; that is, it has the form f sxd − ax3 1 bx2 1 cx 1

d, where a ± 0.

(a) Show that a cubic function can have two, one, or no critical number(s). Give examples and sketches to illustrate the three possibilities.

(b) How many local extreme values can a cubic function have?

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