What is the extreme-x^3+300x+y^3-48y+9 ?

The extreme-x^3+300x+y^3-48y+9 is Minimum(-10,4),Saddle(-10,-4),Saddle(10,4),Maximum(10,-4)

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extreme-x^3+300x+y^3-48y+9

extreme points

- x^{3} + 300 x + y^{3} - 48 y + 9

Minimum (- 10, 4), Saddle (- 10, - 4), Saddle (10, 4), Maximum (10, - 4)

Solution steps

Find the critical points:

(- 10, 4), (- 10, - 4), (10, 4), (10, - 4)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 y

D (x, y) = - 36 x y

Check the sign of at each critical point

Check critical point

(- 10, 4) :

Minimum

Check critical point

(- 10, - 4) :

Saddle

Check critical point

(10, 4) :

Saddle

Check critical point

(10, - 4) :

Maximum

Minimum (- 10, 4), Saddle (- 10, - 4), Saddle (10, 4), Maximum (10, - 4)

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

(5 - 9 t)^{\frac{9}{2}}

f (x) = 5 x^{2} ln (4 x)

f (x) = x + y + x^{2} y + x y^{2}

x^{3} - 48 x y + 64 y^{3}

What is the extreme-x^3+300x+y^3-48y+9 ?
The extreme-x^3+300x+y^3-48y+9 is Minimum(-10,4),Saddle(-10,-4),Saddle(10,4),Maximum(10,-4)