Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 4 - Applications of the Derivative - 4.3 The Mean Value Theorem and Monotonicity - Exercises - Page 190: 53


$a\geq 0$

Work Step by Step

Given $$f(x)=x^{3}+a x+b$$ Since $$f'(x) =3x^{2}+a$$ Since $3x^2\geq 0$, then the condition that guarantees $f'(x)>0$ is $a\geq 0$.
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