What is the extreme f(x,y)=x^2+y^3-300x-75y-3 ?

The extreme f(x,y)=x^2+y^3-300x-75y-3 is Minimum(150,5),Saddle(150,-5)

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extreme f(x,y)=x^2+y^3-300x-75y-3

extreme points

f (x, y) = x^{2} + y^{3} - 300 x - 75 y - 3

Minimum (150, 5), Saddle (150, - 5)

Solution steps

Find the critical points:

(150, 5), (150, - 5)

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

D (x, y) = 12 y

Check the sign of at each critical point

Check critical point

(150, 5) :

Minimum

Check critical point

(150, - 5) :

Saddle

Minimum (150, 5), Saddle (150, - 5)

0.285 x^{2} - 2.28 x + 7.6

f (x) = x ln (\frac{x}{4})

x^{4 - 50 x^{2}}

- 0.06 x^{2} - 0.02 y^{2} - 1.5 x y + 85 x + 69 y

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

What is the extreme f(x,y)=x^2+y^3-300x-75y-3 ?
The extreme f(x,y)=x^2+y^3-300x-75y-3 is Minimum(150,5),Saddle(150,-5)