## Calculus 8th Edition

Published by Cengage

# Chapter 6 - Inverse Functions - 6.2 Exponential Functions and Their Derivatives - 6.2 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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