   Chapter 1.2, Problem 11E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find an expression for a cubic function f if f ( 1 ) = 6 and f ( − 1 ) = f ( 0 ) = f ( 2 ) = 0 .

To determine

To find: An expression for a cubic function which satisfies the given conditions.

Explanation

Given:

The given conditions are f(1)=6,f(1)=f(0)=f(2)=0 .

Observation:

The number a is said to be a zero of an equation when f(a)=0 , where xa is said to be a factor of the equation.

Since f(1)=f(0)=f(2)=0 , −1, 0, 2 are the roots of the linear equation and (x+1)(x0) and (x2) are the factors of the equation.

Thus, f(x)=a(x+1)(x)(x2)

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