What is the extreme f(x,y)=x^3+y^3-300x-243y+2 ?

The extreme f(x,y)=x^3+y^3-300x-243y+2 is Saddle(-10,9),Maximum(-10,-9),Minimum(10,9),Saddle(10,-9)

Popular >

extreme f(x,y)=x^3+y^3-300x-243y+2

extreme points

f (x, y) = x^{3} + y^{3} - 300 x - 243 y + 2

Saddle (- 10, 9), Maximum (- 10, - 9), Minimum (10, 9), Saddle (10, - 9)

Solution steps

Find the critical points:

(- 10, 9), (- 10, - 9), (10, 9), (10, - 9)

\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, 9) :

Saddle

Check critical point

(- 10, - 9) :

Maximum

Check critical point

(10, 9) :

Minimum

Check critical point

(10, - 9) :

Saddle

Saddle (- 10, 9), Maximum (- 10, - 9), Minimum (10, 9), Saddle (10, - 9)

f (x, y) = - 6 x^{2} - 7 x y - 6 y^{2} - 18 x - 58 y + 8

f (x) = \frac{x ^{2}}{144} - \frac{y ^{2}}{81}

25 - x^{2}

f (x) = - x^{3} + x^{2} - 9 x + 8

3 x^{3} + 30 x^{2} + 75 x - 9

What is the extreme f(x,y)=x^3+y^3-300x-243y+2 ?
The extreme f(x,y)=x^3+y^3-300x-243y+2 is Saddle(-10,9),Maximum(-10,-9),Minimum(10,9),Saddle(10,-9)