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35 votes
35 votes
Which polynomial does not have an absolute maximum?

A. 2nd degree
B. 3rd degree
C. 4th degree

User Keyne Viana
by
3.1k points

1 Answer

17 votes
17 votes

Answer: B. 3rd degree

Reason:

Odd degree polynomials do not have an absolute max nor absolute min. The curve stretches forever upward and downward. The range is the set of all real numbers.

Even degree polynomials on the other hand do have a highest point or lowest point, depending on the leading coefficient. If the leading coefficient is negative, then the curve has a highest point. If the leading coefficient is positive, then the curve has a lowest point.

Example: y = x^3 does not have an absolute max, but y = -x^2 does.

User Yashesh
by
2.7k points
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