Answer
False
Work Step by Step
Counter-example:
Let $f(x)=x^5+4x\to f'(x)=5x^4+4$ which is never equal to $0\to$ No critical numbers.
Hence, not every $n$th-degree polynomial has $(n-1)$ critical numbers.
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 3 - Applications of Differentiation - 3.3 Exercises - Page 186: 93
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