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Popular >

extreme x*ln(x)

Solution

extreme points

x \cdot ln (x)

Solution

Minimum (\frac{1}{e}, - \frac{1}{e})

Solution steps

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

Find intervals:

Decreasing

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

Increasing

: \frac{1}{e} < x < \infty

Plug

x = \frac{1}{e}

into

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

Minimum (\frac{1}{e}, - \frac{1}{e})

Popular Examples

extreme f(x)=x^2+xy+y^2 extreme points

f (x) = x^{2} + x y + y^{2}

extreme f(x,y)=3+xy-x-2y extreme points

f (x, y) = 3 + x y - x - 2 y

extreme f(x,y)=x^3+6xy+y^3+3 extreme points

f (x, y) = x^{3} + 6 x y + y^{3} + 3

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

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

extreme x^4-6x^2 extreme points

x^{4} - 6 x^{2}

Frequently Asked Questions (FAQ)

What is the extreme x*ln(x) ?
The extreme x*ln(x) is Minimum(1/e ,-1/e)