What is the extreme F(X,Y)=3X+2X^2+4Y+Y^2-2XY ?

The extreme F(X,Y)=3X+2X^2+4Y+Y^2-2XY is Minimum(-7/2 ,-11/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme F(X,Y)=3X+2X^2+4Y+Y^2-2XY

extreme points

F (X, Y) = 3 X + 2 X^{2} + 4 Y + Y^{2} - 2 X Y

Minimum (- \frac{7}{2}, - \frac{11}{2})

Solution steps

Find the critical points:

(- \frac{7}{2}, - \frac{11}{2})

\frac{\partial ^{2} f}{\partial X ^{2}} = 2

D (X, Y) = 4

Check the sign of at each critical point

Check critical point

(- \frac{7}{2}, - \frac{11}{2}) :

Minimum

Minimum (- \frac{7}{2}, - \frac{11}{2})

f (x) = 8 x^{2} - 6 x^{4}

T (x, y) = 27 - 8 x^{2} - 9 y^{2}

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

f (x) = x^{5} - 5 x + 6

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

What is the extreme F(X,Y)=3X+2X^2+4Y+Y^2-2XY ?
The extreme F(X,Y)=3X+2X^2+4Y+Y^2-2XY is Minimum(-7/2 ,-11/2)