What is the extreme f(x,y)=x^3+y^3-147x-75y-10 ?

The extreme f(x,y)=x^3+y^3-147x-75y-10 is Saddle(-7,5),Maximum(-7,-5),Minimum(7,5),Saddle(7,-5)

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extreme f(x,y)=x^3+y^3-147x-75y-10

extreme points

f (x, y) = x^{3} + y^{3} - 147 x - 75 y - 10

Saddle (- 7, 5), Maximum (- 7, - 5), Minimum (7, 5), Saddle (7, - 5)

Solution steps

Find the critical points:

(- 7, 5), (- 7, - 5), (7, 5), (7, - 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

(- 7, 5) :

Saddle

Check critical point

(- 7, - 5) :

Maximum

Check critical point

(7, 5) :

Minimum

Check critical point

(7, - 5) :

Saddle

Saddle (- 7, 5), Maximum (- 7, - 5), Minimum (7, 5), Saddle (7, - 5)

f (x) = x^{3} - 4 x^{2} - 16 x + 2

f (x) = x^{3} - 4 x^{2} - 16 x - 1

f (x, y) = 400 - 49 x^{2} - 64 y^{2}

f (x) = 2 x ln ∣ x ∣

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

What is the extreme f(x,y)=x^3+y^3-147x-75y-10 ?
The extreme f(x,y)=x^3+y^3-147x-75y-10 is Saddle(-7,5),Maximum(-7,-5),Minimum(7,5),Saddle(7,-5)