A cubic function is a polynomial of degree 3; that is, it has the form f(x) = ax^3 +bx^2 +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?

A cubic function is a polynomial of degree 3; that is, it has the form f(x) = ax^3 +bx^2 +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?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 15E

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