What is the extreme 8xy-2x^4-2y^4 ?

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

Popular >

extreme 8xy-2x^4-2y^4

extreme points

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, y) = 2 x^{2} - 8 x + y^{2} - 8 y + 7

f (x) = \frac{1}{4} x^{4} + \frac{1}{3} x^{3} - x^{2} + 2

f (x) = \frac{3 x - 4}{x ^{2} + 1}, - 2 \leq x \leq 2

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

f (x, y) = 2 x^{2} + y^{2} + 8 x - 6 y - 2 x y + 12

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