Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 3 - Applications of Differentiation - 3.1 Maximum and Minimum Values - 3.1 Execises - Page 211: 32


No critical numbers

Work Step by Step

Find the critical numbers for $f(x) = 2x^3+x^2+2x$ Differentiate and set the derivative $=0$ $f'(x) = 6x^2+2x+2$ $0=2(3x^2+x+1)$ $b^2-4ac = 1-4(3)(1) = -11$ The discriminant of the right hand side quadratic is $<0$. Therefore, the right hand side will never $=0$, so $f(x) $ has no critical numbers.
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