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Popular >

extreme (ln(x))/x

Solution

extreme points

\frac{ln ( x )}{x}

Solution

Maximum (e, \frac{1}{e})

Solution steps

f^{'} (x) = \frac{1 - ln ( x )}{x ^{2}}

Find intervals:

Increasing

: 0 < x < e,

Decreasing

: e < x < \infty

Plug

x = e

into

\frac{ln ( x )}{x} : \frac{1}{e}

Maximum (e, \frac{1}{e})

Popular Examples

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f (x, y) = x y^{2} + 3 x^{3} y - x y

extreme x^4-2x^2 extreme points

x^{4} - 2 x^{2}

extreme f(x)=e^x+x^2 extreme points

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

extreme f(x,y)=x^2+xy+y^2 extreme points

f (x, y) = x^{2} + x y + y^{2}

extreme f(x,y)=x^3+6xy+3y^2 extreme points

f (x, y) = x^{3} + 6 x y + 3 y^{2}

Frequently Asked Questions (FAQ)

What is the extreme (ln(x))/x ?
The extreme (ln(x))/x is Maximum(e, 1/e)