What is the extreme f(x)=(e^x)/((5x)),x>0 ?

The extreme f(x)=(e^x)/((5x)),x>0 is Minimum(1, e/5)

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extreme f(x)=(e^x)/((5x)),x>0

extreme points

f (x) = \frac{e ^{x}}{( 5 x )}, x > 0

Minimum (1, \frac{e}{5})

Solution steps

Find the critical points:

x = 1

Domain of

\frac{e ^{x}}{5 x}, x > 0 : x > 0

Find intervals:

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug the extreme point

x = 1

into

\frac{e ^{x}}{5 x} \Rightarrow y = \frac{e}{5}

Minimum (1, \frac{e}{5})

f (x) = \frac{x}{x ^{3} - 1}

\frac{8 x - 3}{x}

f (x) = \frac{1}{x + 14}

f (x) = \frac{- 3 x + 27}{x - 8}

(\frac{1}{2} x - 1)^{2} - 2

What is the extreme f(x)=(e^x)/((5x)),x>0 ?
The extreme f(x)=(e^x)/((5x)),x>0 is Minimum(1, e/5)