What is the extreme 4xy-x^4-y^4 ?

The extreme 4xy-x^4-y^4 is Saddle(0,0),Maximum(-1,-1),Maximum(1,1)

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extreme 4xy-x^4-y^4

extreme points

4 x y - x^{4} - y^{4}

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

Solution steps

Find the critical points:

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

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

D (x, y) = 144 x^{2} y^{2} - 16

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(- 1, - 1) :

Maximum

Check critical point

(1, 1) :

Maximum

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

(x + 2)^{\frac{2}{3}}

f (x) = x^{3} - 3 x^{2} - 24 x

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

f (x) = 9 x^{3} - \frac{1}{x ^{3}}

What is the extreme 4xy-x^4-y^4 ?
The extreme 4xy-x^4-y^4 is Saddle(0,0),Maximum(-1,-1),Maximum(1,1)