What is the extreme f(x,y)=x^3+y^3-300x-75y-3 ?

The extreme f(x,y)=x^3+y^3-300x-75y-3 is Saddle(-10,5),Maximum(-10,-5),Minimum(10,5),Saddle(10,-5)

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extreme f(x,y)=x^3+y^3-300x-75y-3

extreme points

f (x, y) = x^{3} + y^{3} - 300 x - 75 y - 3

Saddle (- 10, 5), Maximum (- 10, - 5), Minimum (10, 5), Saddle (10, - 5)

Solution steps

Find the critical points:

(- 10, 5), (- 10, - 5), (10, 5), (10, - 5)

\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, 5) :

Saddle

Check critical point

(- 10, - 5) :

Maximum

Check critical point

(10, 5) :

Minimum

Check critical point

(10, - 5) :

Saddle

Saddle (- 10, 5), Maximum (- 10, - 5), Minimum (10, 5), Saddle (10, - 5)

f (x) = x^{2} + \frac{12}{x}

f (x) = 7 cos (x), 0 \leq x \leq 2 π

f (x) = x^{3} - 12 x^{2} - 27 x + 10, - 2 \leq x \leq 0

f (x, y) = - 7 x^{2} - 3 y^{2} + 7 x - 6 y + 8

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

What is the extreme f(x,y)=x^3+y^3-300x-75y-3 ?
The extreme f(x,y)=x^3+y^3-300x-75y-3 is Saddle(-10,5),Maximum(-10,-5),Minimum(10,5),Saddle(10,-5)