What is the extreme f(x)=x^2+y^2+x^2y+7 ?

The extreme f(x)=x^2+y^2+x^2y+7 is Minimum(0,0),Saddle(sqrt(2),-1),Saddle(-sqrt(2),-1)

Popular >

extreme f(x)=x^2+y^2+x^2y+7

extreme points

f (x) = x^{2} + y^{2} + x^{2} y + 7

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}} = 2

D (x, y) = 2 (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) = - \frac{3}{2} x + 3

f (x, y) = - 4 x^{2} - 8 y^{2} + 4 x - 16 y + 1

x + 4 - x^{2}

2000 - 10 x \cdot e^{5 \cdot (\frac{x ^{2}}{8})}

f (x) = 3 x^{2} - 3 y^{2} + 6 = 0

What is the extreme f(x)=x^2+y^2+x^2y+7 ?
The extreme f(x)=x^2+y^2+x^2y+7 is Minimum(0,0),Saddle(sqrt(2),-1),Saddle(-sqrt(2),-1)