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Popular >

extreme f(x)=3xln(x)

Solution

extreme points

f (x) = 3 x ln (x)

Solution

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

Solution steps

f^{'} (x) = 3 (ln (x) + 1)

Find intervals:

Decreasing

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

Increasing

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

Plug

x = \frac{1}{e}

into

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

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

Popular Examples

extreme f(x,y)=5x^2+5y^2+5xy-10x-5y+18 extreme points

f (x, y) = 5 x^{2} + 5 y^{2} + 5 x y - 10 x - 5 y + 18

extreme f(x,y)=x^3+3xy^2-15x^2-15y^2+72x extreme points

f (x, y) = x^{3} + 3 x y^{2} - 15 x^{2} - 15 y^{2} + 72 x

extreme f(x,y)=10-4x-5y extreme points

f (x, y) = 10 - 4 x - 5 y

extreme f(x,y)=x^2-1/2 y^2+3x extreme points

f (x, y) = x^{2} - \frac{1}{2} y^{2} + 3 x

extreme f(x,y)=x^2-3xy+6y^2+5x-2y+8 extreme points

f (x, y) = x^{2} - 3 x y + 6 y^{2} + 5 x - 2 y + 8

Frequently Asked Questions (FAQ)

What is the extreme f(x)=3xln(x) ?
The extreme f(x)=3xln(x) is Minimum(1/e ,-3/e)