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Popular Functions >

extreme f(x)= x/(ln(2x))

Solution

extreme

Solution

Minimum (\frac{e}{2}, \frac{e}{2})

Solution steps

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

Find intervals:

Decreasing

: 0 < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < \frac{e}{2},

Increasing

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

Plug

x = \frac{e}{2}

into

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

Minimum (\frac{e}{2}, \frac{e}{2})

Graph

Popular Examples

extreme f(x,y)=4-x^2-y^2+xy+x

extreme f(x)=(x^2)/(x^2+3),-1<= x<= 1

extreme f(x)=(x^2)/(x^2+1),-2<= x<= 2

extreme f(x,y)=9x^2+3xy+9y^2+7xy^2+3x^2y

extreme y=-5x^2-6x+2

Frequently Asked Questions (FAQ)

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