What is the extreme (e^{3.4x})/(x^3) ?

The extreme (e^{3.4x})/(x^3) is Minimum(15/17 ,29.23859…)

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extreme (e^{3.4x})/(x^3)

extreme points

\frac{e ^{3.4 x}}{x ^{3}}

Minimum (\frac{15}{17}, 29.23859 \dots)

Solution steps

f^{'} (x) = \frac{e ^{3.4 x} ( 3.4 x - 3 )}{x ^{4}}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{15}{17},

Increasing

: \frac{15}{17} < x < \infty

Plug

x = \frac{15}{17}

into

\frac{e ^{3.4 x}}{x ^{3}} : 29.23859 \dots

Minimum (\frac{15}{17}, 29.23859 \dots)

f (x) = - x^{2} + x - 2

- 2 x^{3} + 3 x^{2}

f (x) = x^{3} - 3 x + 3, 0 \leq x \leq 2

f (x, y) = 2 x y - \frac{1}{2} (x^{4} + y^{4}) + 1

f (x, y) = x + y + \frac{1}{x} + \frac{4}{y}

What is the extreme (e^{3.4x})/(x^3) ?
The extreme (e^{3.4x})/(x^3) is Minimum(15/17 ,29.23859…)