A cubic function is a polynomial of degree 3; that is, it hasthe form f(x)  =ax3 + bx2 +cx + d , where a≠ 0 .(a) Show that a cubic function can have two, one, or nocritical number(s). Give examples and sketches to illustratethe three possibilities.(b) How many local extreme values can a cubic functionhave?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 50E
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A cubic function is a polynomial of degree 3; that is, it has
the form f(x)  =ax3 + bx2 +cx + 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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