What is the extreme f(x)=(e^x)/(x^3) ?

The extreme f(x)=(e^x)/(x^3) is Minimum(3,(e^3)/(27))

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extreme f(x)=(e^x)/(x^3)

extreme

Minimum (3, \frac{e ^{3}}{27})

Solution steps

f^{'} (x) = \frac{e ^{x} ( x - 3 )}{x ^{4}}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 3

into

\frac{e ^{x}}{x ^{3}} : \frac{e ^{3}}{27}

Minimum (3, \frac{e ^{3}}{27})

What is the extreme f(x)=(e^x)/(x^3) ?
The extreme f(x)=(e^x)/(x^3) is Minimum(3,(e^3)/(27))