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Popular Functions >

extreme sqrt(x)ln(4x)

Solution

extreme

Solution

Minimum (\frac{1}{4 e ^{2}}, - \frac{1}{e})

Solution steps

f^{'} (x) = \frac{ln ( 4 x )}{2 x} + \frac{1}{x}

Find intervals:

Decreasing

: 0 < x < \frac{1}{4 e ^{2}},

Increasing

: \frac{1}{4 e ^{2}} < x < \infty

Plug

x = \frac{1}{4 e ^{2}}

into

x ln (4 x) : - \frac{1}{e}

Minimum (\frac{1}{4 e ^{2}}, - \frac{1}{e})

Graph

Popular Examples

extreme f(x)=2x^2+7x

extreme f(x)=(x^2+3x+9),-2<= x<= 1

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

Frequently Asked Questions (FAQ)

What is the extreme sqrt(x)ln(4x) ?
The extreme sqrt(x)ln(4x) is Minimum(1/(4e^2),-1/e)