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Popular >

extreme (2x)/(ln(x))

Solution

extreme points

\frac{2 x}{ln ( x )}

Solution

Minimum (e, 2 e)

Solution steps

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

Find intervals:

Decreasing

: 0 < x < 1,

Decreasing

: 1 < x < e,

Increasing

: e < x < \infty

Plug

x = e

into

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

Minimum (e, 2 e)

Popular Examples

extreme f(x)=12+2x-x^2,0<= x<= 5 extreme points

f (x) = 12 + 2 x - x^{2}, 0 \leq x \leq 5

extreme f(x)=4x+y extreme points

f (x) = 4 x + y

extreme f(x)=1-sqrt(x)extreme points

f (x) = 1 - x

extreme f(x,y)=x^2+xy+y^2+3x-3y+7 extreme points

f (x, y) = x^{2} + x y + y^{2} + 3 x - 3 y + 7

extreme f(x,y)= x/(1-x^2-y^2)extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme (2x)/(ln(x)) ?
The extreme (2x)/(ln(x)) is Minimum(e,2e)