Calculus (3rd Edition)

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

Chapter 4 - Applications of the Derivative - 4.2 Extreme Values - Exercises - Page 181: 25

Answer

Minimum value is 3 at $ x=-1$ and maximum value is 21 at $ x=2$.

Work Step by Step

$ f'(x)= 4x+4$ $ f $ is differentiable everywhere. So, the only critical point we get is $ c $ such that $ f'(c)=0$ i.e., $4c+4=0\implies 4c=-4\implies c=-1$ To find maximum and minimum values, we compare values at the critical point and end points. $ f(-1)=2(-1)^{2}+4(-1)+5=3$ $ f(-2)= 2(-2)^{2}+4(-2)+5=5$ $ f(2)=2(2)^{2}+4(2)+5=21$ Minimum value is 3 at $ x=-1$ and maximum value is 21 at $ x=2$
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