Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.5 Higher Derivatives - Preliminary Questions - Page 135: 3


All the polynomials of the form: $$ f(x)=a_0+a_1x+a_2x^2.$$

Work Step by Step

Any polynomial $ f(x)$ of degree $2$ is given by $$ f(x)=a_0+a_1x+a_2x^2.$$ Now, we have $$ f'(x)=a_1+2a_2x, \quad f''(x)=2a_2$$ and hence $ f'''(x)=0$ for all $ x $.
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