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Popular >

inflection (ln(x))/x

Solution

inflection points

\frac{ln ( x )}{x}

Solution

(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}}})

Popular Examples

monotone (x^2+2x-1)(2x^2-3x+6)monotone intervals

(x^{2} + 2 x - 1) (2 x^{2} - 3 x + 6)

extreme f(x)=4-x^2 extreme points

f (x) = 4 - x^{2}

domain of f(x)=5x-10 domain

f (x) = 5 x - 10

inverse of y=x^2-4x inverse

y = x^{2} - 4 x

asymptotes of f(x)=(x^4-16)/(2x^2-4x)asymptotes

f (x) = \frac{x ^{4} - 16}{2 x ^{2} - 4 x}

Frequently Asked Questions (FAQ)

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