What is the extreme f(x,y)=3x^3-5y^2-225x+70y+23 ?

The extreme f(x,y)=3x^3-5y^2-225x+70y+23 is Maximum(-5,7),Saddle(5,7)

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extreme f(x,y)=3x^3-5y^2-225x+70y+23

extreme points

f (x, y) = 3 x^{3} - 5 y^{2} - 225 x + 70 y + 23

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

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = - 10

D (x, y) = - 180 x

Check the sign of at each critical point

Check critical point

(- 5, 7) :

Maximum

Check critical point

(5, 7) :

Saddle

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

What is the extreme f(x,y)=3x^3-5y^2-225x+70y+23 ?
The extreme f(x,y)=3x^3-5y^2-225x+70y+23 is Maximum(-5,7),Saddle(5,7)