What is the extreme f(x,y)=2xy-6y^2+x^2y-3y+7 ?

The extreme f(x,y)=2xy-6y^2+x^2y-3y+7 is Saddle(1,0),Saddle(-3,0),Maximum(-1,-1/3)

Popular >

extreme f(x,y)=2xy-6y^2+x^2y-3y+7

extreme points

f (x, y) = 2 x y - 6 y^{2} + x^{2} y - 3 y + 7

Saddle (1, 0), Saddle (- 3, 0), Maximum (- 1, - \frac{1}{3})

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = - 12

D (x, y) = - 24 y - 4 x^{2} - 8 x - 4

Check the sign of at each critical point

Check critical point

(1, 0) :

Saddle

Check critical point

(- 3, 0) :

Saddle

Check critical point

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

Maximum

Saddle (1, 0), Saddle (- 3, 0), Maximum (- 1, - \frac{1}{3})

f (x) = 2 x^{4} - x^{2} + 5

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

y = 6 x^{4} + 8 x^{3}

πj z + 3 w

f (x) = 4 (x - e^{x})

What is the extreme f(x,y)=2xy-6y^2+x^2y-3y+7 ?
The extreme f(x,y)=2xy-6y^2+x^2y-3y+7 is Saddle(1,0),Saddle(-3,0),Maximum(-1,-1/3)