Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.3 Introduction To Techniques Of Differentiation - Exercises Set 2.3: 34

Answer

True.

Work Step by Step

A cubic function is any function where the highest degree is three, so it can be written as any function $f(x)=ax^3+bx^2+cx+d$, where $a\ne0$. The derivative of $f(x)$ is $f'(x)=3ax^2+2bx+c$. A quadratic polynomial is a polynomial whose highest degree is two. Since $a$ cannot equal zero, the highest degree must be two and the derivative must be a quadratic polynomial.
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