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Popular >

extreme y=(ln(x))/x

Solution

extreme points

y = \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

extreme x^2+y^2+x^2y+4 extreme points

x^{2} + y^{2} + x^{2} y + 4

extreme f(x)=4x^5-8x^4-5x^3+10x^2+x-2 extreme points

f (x) = 4 x^{5} - 8 x^{4} - 5 x^{3} + 10 x^{2} + x - 2

extreme f(x)=8x-9x^{8/9}extreme points

f (x) = 8 x - 9 x^{\frac{8}{9}}

extreme f(x,y)=50y^2+x^2-x^2y extreme points

f (x, y) = 50 y^{2} + x^{2} - x^{2} y

extreme f(x,y)=sqrt(4-4x^2-y^2)extreme points

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

Frequently Asked Questions (FAQ)

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