Concept explainers
To determine: Does a cubic function always, sometimes, or never have a turning point? Justify your answer.
A cubic function has a turning point “sometimes”.
Explanation:
It is known that a polynomial function with degree n has at-most
It is also known that an odd degree polynomial has an even number of turning points with a minimum of 0 turning points. While an even degree polynomial has an odd number of turning points with a minimum of 1 turning point.
A cubic function is an odd degree polynomial, so it will have a minimum of 0 turning points. This means that cubic functions do not have a turning point always.
Therefore, cubic function has a turning point “sometimes”.
Chapter 2 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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