What is the inflection f(x)=(ln(x))/x ?

The inflection f(x)=(ln(x))/x is (e^{3/2}, 3/(2e^{3/2)})

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inflection f(x)=(ln(x))/x

inflection points

f (x) = \frac{ln ( x )}{x}

(e^{\frac{3}{2}}, \frac{3}{2 e ^{\frac{3}{2}}})

Solution steps

f^{''} (x) = - \frac{- 2 ln ( x ) + 3}{x ^{3}}

Find intervals:

Concave Downward

: 0 < x < e^{\frac{3}{2}},

Concave Upward

: e^{\frac{3}{2}} < x < \infty

Plug

x = e^{\frac{3}{2}}

into

\frac{ln ( x )}{x} : \frac{3}{2 e ^{\frac{3}{2}}}

(e^{\frac{3}{2}}, \frac{3}{2 e ^{\frac{3}{2}}})

(1992, 61.6), (1997, 64)

- 3 x + 2 y = 6

(- 6, 6), (- 3, 3)

f (x) = \frac{4 - 3 x}{x - 7}

\frac{1}{x ^{2} + 2 x}

What is the inflection f(x)=(ln(x))/x ?
The inflection f(x)=(ln(x))/x is (e^{3/2}, 3/(2e^{3/2)})