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: 68

Answer

$e$

Work Step by Step

Need to find the absolute minimum value of the function $g(x) =\frac{e^{x}}{x} $ , $x>0$ Take first derivative of the function. Apply quotient rule. $g'(x) =\frac{xe^{x}-e^{x}}{x^{2}} $ , $x>0$ $x>1$ satisfies the given domain $x>0$ Thus, as per first derivative test the absolute minimum value is $g(1) =\frac{e^{1}}{1} $ , $x>0$ Hence, $e$ is the absolute minimum value of the function.
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