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Popular >

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

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Plug

x = \frac{2}{e}

into

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

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

Graph

Popular Examples

extreme f(x)= 1/2 (3x-1)extreme points

f (x) = \frac{1}{2} (3 x - 1)

extreme f(x)=3x^3-5x^2+x+3 extreme points

f (x) = 3 x^{3} - 5 x^{2} + x + 3

extreme u(x,y)=y^2e^x+3x^2 extreme points

u (x, y) = y^{2} e^{x} + 3 x^{2}

extreme f(x)=-(2x)/(5x^2+8)extreme points

f (x) = - \frac{2 x}{5 x ^{2} + 8}

extreme f(x)=2x^3+6x-90x+5,-5<x<4 extreme points

f (x) = 2 x^{3} + 6 x - 90 x + 5, - 5 < x < 4

Frequently Asked Questions (FAQ)

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