What is the extreme f(x,y)=-4xy+2x^2-10y^2-4y^3-1 ?

The extreme f(x,y)=-4xy+2x^2-10y^2-4y^3-1 is Minimum(-2,-2),Saddle(0,0)

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extreme f(x,y)=-4xy+2x^2-10y^2-4y^3-1

extreme points

f (x, y) = - 4 x y + 2 x^{2} - 10 y^{2} - 4 y^{3} - 1

Minimum (- 2, - 2), Saddle (0, 0)

Solution steps

Find the critical points:

(- 2, - 2), (0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 24 y - 20

D (x, y) = - 96 y - 96

Check the sign of at each critical point

Check critical point

(- 2, - 2) :

Minimum

Check critical point

(0, 0) :

Saddle

Minimum (- 2, - 2), Saddle (0, 0)

4 sin (2 x), - 2 π \leq x \leq π

0.3 x^{2} - 66 x + 15239

a (- 6 - 0)^{2}

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

f (x) = 4 sec (x)

What is the extreme f(x,y)=-4xy+2x^2-10y^2-4y^3-1 ?
The extreme f(x,y)=-4xy+2x^2-10y^2-4y^3-1 is Minimum(-2,-2),Saddle(0,0)