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

The extreme x^2y-x^2-2y^2 is Maximum(0,0),Saddle(2,1),Saddle(-2,1)

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extreme x^2y-x^2-2y^2

extreme points

x^{2} y - x^{2} - 2 y^{2}

Maximum (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) :

Maximum

Check critical point

(2, 1) :

Saddle

Check critical point

(- 2, 1) :

Saddle

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

f (x) = 3 - 4 sin (3 x)

f (x, y) = ln ∣ 4 - x - y ∣

f (x) = (x^{2} - 1)^{4}

f (x) = - x^{3} - x^{2} + 5 x

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

What is the extreme x^2y-x^2-2y^2 ?
The extreme x^2y-x^2-2y^2 is Maximum(0,0),Saddle(2,1),Saddle(-2,1)