What is the extreme f(x)=8(xy)-2x^4-2y^4 ?

The extreme f(x)=8(xy)-2x^4-2y^4 is Saddle(0,0),Maximum(-1,-1),Maximum(1,1)

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extreme f(x)=8(xy)-2x^4-2y^4

extreme points

f (x) = 8 (x y) - 2 x^{4} - 2 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}} = - 24 y^{2}

D (x, y) = 576 x^{2} y^{2} - 64

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)

f (x) = 3 x^{3} + 3 x^{2} - 10 x - 2

f (x) = 0.0001 x^{2} + 3.2 x - 90

f (x, y) = θ

\frac{x ^{3}}{3} - x^{2} - 35 x + 4

f (x, y) = e^{6 x^{2} + 4 y^{2} + 10}

What is the extreme f(x)=8(xy)-2x^4-2y^4 ?
The extreme f(x)=8(xy)-2x^4-2y^4 is Saddle(0,0),Maximum(-1,-1),Maximum(1,1)