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Popular >

extreme x^x

Solution

extreme points

x^{x}

Solution

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

Solution steps

f^{'} (x) = x^{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^{x} : (\frac{1}{e})^{\frac{1}{e}}

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

Popular Examples

extreme x^4-6x^3 extreme points

x^{4} - 6 x^{3}

extreme f(x)=x^{2/3}(x^2-4)extreme points

f (x) = x^{\frac{2}{3}} (x^{2} - 4)

extreme P(x,y)=4x^2-100y^2 extreme points

P (x, y) = 4 x^{2} - 100 y^{2}

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

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

extreme f(x,y)=x^2\times y^3-10y+15xy^2 extreme points

f (x, y) = x^{2} \times y^{3} - 10 y + 15 x y^{2}

Frequently Asked Questions (FAQ)

What is the extreme x^x ?
The extreme x^x is Minimum(1/e ,(1/e)^{1/e})