What is the extreme x^2y-6y^2-3x^2 ?

The extreme x^2y-6y^2-3x^2 is Maximum(0,0),Saddle(6,3),Saddle(-6,3)

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extreme x^2y-6y^2-3x^2

extreme points

x^{2} y - 6 y^{2} - 3 x^{2}

Maximum (0, 0), Saddle (6, 3), Saddle (- 6, 3)

Solution steps

Find the critical points:

(0, 0), (6, 3), (- 6, 3)

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

D (x, y) = - 12 (2 y - 6) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Check critical point

(6, 3) :

Saddle

Check critical point

(- 6, 3) :

Saddle

Maximum (0, 0), Saddle (6, 3), Saddle (- 6, 3)

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

f (x) = x^{3} + x^{2} - 46 x + 80

f (x) = 3 x^{4} + 8 x^{3} - 6 x^{2} + 24 x

3 x (x - 3)^{3}

f (x) = x^{\frac{4}{3}} + 4^{\frac{1}{3}}

What is the extreme x^2y-6y^2-3x^2 ?
The extreme x^2y-6y^2-3x^2 is Maximum(0,0),Saddle(6,3),Saddle(-6,3)