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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Answered: A polynomial function of degree n(n 2…

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Calculus

A polynomial function of degree n(n 2 3) can have at most (n - 2) inflection points.

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

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Concept explainers

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

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.

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