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Popular Functions >

extreme f(x)=(ln(5x))/x

Solution

extreme

Solution

Maximum (\frac{e}{5}, \frac{5}{e})

Solution steps

f^{'} (x) = \frac{1 - ln ( 5 x )}{x ^{2}}

Find intervals:

Increasing

: 0 < x < \frac{e}{5},

Decreasing

: \frac{e}{5} < x < \infty

Plug

x = \frac{e}{5}

into

\frac{ln ( 5 x )}{x} : \frac{5}{e}

Maximum (\frac{e}{5}, \frac{5}{e})

Graph

Popular Examples

extreme f(x,y)=x^2-4x-y^2-6y+7

extreme f(x)=x^5-5x^4+5=x^4(x-5)+5

extreme f(x,y)=2xy-x^2-6y^2+4x+1

extreme f(x)=-x^2-2x+99

extreme f(t)=te^{w/t}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(ln(5x))/x ?
The extreme f(x)=(ln(5x))/x is Maximum(e/5 , 5/e)