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Popular >

extreme xln(x^2)

Solution

extreme points

x ln (x^{2})

Solution

Maximum (- \frac{1}{e}, \frac{2}{e}), Minimum (\frac{1}{e}, - \frac{2}{e})

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{1}{e}

into

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

Maximum (- \frac{1}{e}, \frac{2}{e})

Plug

x = \frac{1}{e}

into

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

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

Maximum (- \frac{1}{e}, \frac{2}{e}), Minimum (\frac{1}{e}, - \frac{2}{e})

Popular Examples

extreme 8x+2/x extreme points

8 x + \frac{2}{x}

extreme P(x,y)=2x+4y extreme points

P (x, y) = 2 x + 4 y

extreme f(x)=x^3-y^3+6xy-10 extreme points

f (x) = x^{3} - y^{3} + 6 x y - 10

extreme f(x)=(4860)/x+11x+710272 extreme points

f (x) = \frac{4860}{x} + 11 x + 710272

extreme f(x,y)=(4-xy)/(2+x^2y^2)extreme points

f (x, y) = \frac{4 - x y}{2 + x ^{2} y ^{2}}

Frequently Asked Questions (FAQ)

What is the extreme xln(x^2) ?
The extreme xln(x^2) is Maximum(-1/e , 2/e),Minimum(1/e ,-2/e)