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Popular >

extreme sqrt(x)ln(9x)

Solution

extreme points

x ln (9 x)

Solution

Minimum (\frac{1}{9 e ^{2}}, - \frac{2}{3 e})

Solution steps

f^{'} (x) = \frac{ln ( 9 x )}{2 x} + \frac{1}{x}

Find intervals:

Decreasing

: 0 < x < \frac{1}{9 e ^{2}},

Increasing

: \frac{1}{9 e ^{2}} < x < \infty

Plug

x = \frac{1}{9 e ^{2}}

into

x ln (9 x) : - \frac{2}{3 e}

Minimum (\frac{1}{9 e ^{2}}, - \frac{2}{3 e})

Popular Examples

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

f (x) = 3 x^{2} + 8, - 4 \leq x \leq 4

extreme f(x)=x((3600)/(x-4)+2*10^{-3})extreme points

f (x) = x (\frac{3600}{x - 4} + 2 \cdot 1 0^{- 3})

extreme f(x)=x^2-18ln(x)extreme points

f (x) = x^{2} - 18 ln (x)

extreme f(x,y)=5x^2+5y^2+20x-10y extreme points

f (x, y) = 5 x^{2} + 5 y^{2} + 20 x - 10 y

extreme f(x,y)=xy+pi/8 x^2 extreme points

f (x, y) = x y + \frac{π}{8} x^{2}

Frequently Asked Questions (FAQ)

What is the extreme sqrt(x)ln(9x) ?
The extreme sqrt(x)ln(9x) is Minimum(1/(9e^2),-2/(3e))