What is the extreme f(x,y)=yx^2+2y^2+x^2 ?

The extreme f(x,y)=yx^2+2y^2+x^2 is Minimum(0,0),Saddle(2,-1),Saddle(-2,-1)

Popular >

extreme f(x,y)=yx^2+2y^2+x^2

extreme points

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

Minimum (0, 0), Saddle (2, - 1), Saddle (- 2, - 1)

Solution steps

Find the critical points:

(0, 0), (2, - 1), (- 2, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 4

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(2, - 1) :

Saddle

Check critical point

(- 2, - 1) :

Saddle

Minimum (0, 0), Saddle (2, - 1), Saddle (- 2, - 1)

f (x) = - x^{2} + 8, - 2 \leq x \leq 4

f (x) = - x^{4} + 4 x^{3} + 9 x - 6

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

f (x, y) = - 3 x^{2} - 6 y^{2} - 6 x y + 66 x + 102 y

89 e^{x^{4}}

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