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Popular >

extreme 3x^2ln(x)

Solution

extreme points

3 x^{2} ln (x)

Solution

Minimum (\frac{1}{e}, - \frac{3}{2 e})

Solution steps

f^{'} (x) = 3 (2 x ln (x) + x)

Find intervals:

Decreasing

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

Increasing

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

Plug

x = \frac{1}{e}

into

3 x^{2} ln (x) : - \frac{3}{2 e}

Minimum (\frac{1}{e}, - \frac{3}{2 e})

Popular Examples

extreme f(x,y)=6xy-x^3-3y^2 extreme points

f (x, y) = 6 x y - x^{3} - 3 y^{2}

extreme f(x)=8y^2+5x^2-10y+6x-10 extreme points

f (x) = 8 y^{2} + 5 x^{2} - 10 y + 6 x - 10

extreme f(x)=2x^3-3x^2-12x-1 extreme points

f (x) = 2 x^{3} - 3 x^{2} - 12 x - 1

extreme f(x,y)=x^3+y^2+3/2 x^2-6x-4y+3 extreme points

f (x, y) = x^{3} + y^{2} + \frac{3}{2} x^{2} - 6 x - 4 y + 3

extreme f(x)=2x^3+3x^2-36x+5 extreme points

f (x) = 2 x^{3} + 3 x^{2} - 36 x + 5

Frequently Asked Questions (FAQ)

What is the extreme 3x^2ln(x) ?
The extreme 3x^2ln(x) is Minimum(1/(sqrt(e)),-3/(2e))