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Popular >

extreme x^8ln(x)

Solution

extreme points

x^{8} ln (x)

Solution

Minimum (\frac{1}{8 e}, - \frac{1}{8 e})

Solution steps

f^{'} (x) = 8 x^{7} ln (x) + x^{7}

Find intervals:

Decreasing

: 0 < x < \frac{1}{8 e},

Increasing

: \frac{1}{8 e} < x < \infty

Plug

x = \frac{1}{8 e}

into

x^{8} ln (x) : - \frac{1}{8 e}

Minimum (\frac{1}{8 e}, - \frac{1}{8 e})

Graph

Popular Examples

extreme f(x)=x^6+4x^5+10 extreme points

f (x) = x^{6} + 4 x^{5} + 10

extreme F(x,y)=2x^5+x^3y^2+6xy^4 extreme points

F (x, y) = 2 x^{5} + x^{3} y^{2} + 6 x y^{4}

extreme f(x)=(9x)/(x^2+9)extreme points

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

extreme f(x)=-6x^2+30x-36 extreme points

f (x) = - 6 x^{2} + 30 x - 36

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

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

Frequently Asked Questions (FAQ)

What is the extreme x^8ln(x) ?
The extreme x^8ln(x) is Minimum(1/(\sqrt[8]{e)},-1/(8e))