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Popular >

extreme x^4+3xy^3-xy

Solution

extreme points

x^{4} + 3 x y^{3} - x y

Solution

Solution steps

Find the critical points:

\frac{\partial ^{2} f}{\partial x ^{2}} = 18 x y

D (x, y) = 216 x^{3} y - 81 y^{4} + 18 y^{2} - 1

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(0, - \frac{1}{3}) :

Saddle

Check critical point

(0, \frac{1}{3}) :

Saddle

Check critical point

Minimum

Check critical point

Minimum

Popular Examples

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

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

extreme y=x^2+(z-1)^2 extreme points

y = x^{2} + (z - 1)^{2}

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

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

extreme x^2e^x extreme points

x^{2} e^{x}

extreme f(x)=5+54x-2x^3 extreme points

f (x) = 5 + 54 x - 2 x^{3}

Frequently Asked Questions (FAQ)

What is the extreme x^4+3xy^3-xy ?
The extreme x^4+3xy^3-xy is