College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.5: Zeros Of Polynomial Functions
Problem 79E
Related questions
Question
![Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
A polynomial function of degree n(n 2 3) can have at most (n
- 2) inflection points.
|
True. Suppose the degree of P is n(n 2 3). Thus P"(x)
= 0 can have at most (n – 2) zeros.
True. Suppose the degree of P is n(n > 3). Then P'(x) = 0 can have at most (n – 2) zeros.
False. A polynomial function of degree n(n 2 3) can have at most n inflection points.
False. The polynomial function f(x)
x(x + 1)3, of degree n =
4, has 3 = n – 1 inflection points.
-
False. A polynomial function of degree n(n > 3) can have at most (n
· 2) relative extrema.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F102e4ee8-6845-42b8-bac7-4ba0ca89d711%2Fa00e012f-763d-4ad5-924d-0b6c0c4ceb3c%2Fut91p7p_processed.png&w=3840&q=75)
Transcribed Image Text:Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
A polynomial function of degree n(n 2 3) can have at most (n
- 2) inflection points.
|
True. Suppose the degree of P is n(n 2 3). Thus P"(x)
= 0 can have at most (n – 2) zeros.
True. Suppose the degree of P is n(n > 3). Then P'(x) = 0 can have at most (n – 2) zeros.
False. A polynomial function of degree n(n 2 3) can have at most n inflection points.
False. The polynomial function f(x)
x(x + 1)3, of degree n =
4, has 3 = n – 1 inflection points.
-
False. A polynomial function of degree n(n > 3) can have at most (n
· 2) relative extrema.
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