Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises: 67

Answer

$-1$

Work Step by Step

Need to find the absolute maximum value of the function $f(x) =x-e^{x} $ $f'(x) =1-e^{x}=0$ This implies $e^{x} -1=0$ Thus $x=0$ $f'(x) $ will be increasing for all $x<0$ and $f'(x) $ will be decreasing when $x>0$. Therefore, by first derivative test for absolute extreme values, $f(x) =x-e^{x} $ has an absolute maximum value at x = 0 and absolute maximum value of $f(x) =x-e^{x} $ is $f(0) = 0-1 = -1$ at $x=0$.
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