Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Polynomials
Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.
Question

Using the techniques from Section 3.2, sketch the graph of the polynomial function. Specify the x- and y-intercepts, and also specify the zeros of P(x).

P(x) = −(x + 1)2(x − 1)3(x − 2)
 
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Step 1

Given function is

Calculus homework question answer, step 1, image 1

 

Step 2

Domain of P(x) is

Calculus homework question answer, step 2, image 1

Roots of P(x) are

Calculus homework question answer, step 2, image 2

 

Step 3

Points at which P(x) cuts x axis are those points where P(x) is 0.

Calculus homework question answer, step 3, image 1

Therefore, function P(x) intercepts x axis at

Calculus homework question answer, step 3, image 2

Putting x=0 gives us the y-intercept

Calculus homework question answer, step 3, image 3

 

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