What is the extreme f(x,y)=x^3+y^2-4xy+17x-10y+8 ?

The extreme f(x,y)=x^3+y^2-4xy+17x-10y+8 is Minimum(3,11),Saddle(-1/3 , 13/3)

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extreme f(x,y)=x^3+y^2-4xy+17x-10y+8

extreme points

f (x, y) = x^{3} + y^{2} - 4 x y + 17 x - 10 y + 8

Minimum (3, 11), Saddle (- \frac{1}{3}, \frac{13}{3})

Solution steps

Find the critical points:

(3, 11), (- \frac{1}{3}, \frac{13}{3})

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

D (x, y) = 12 x - 16

Check the sign of at each critical point

Check critical point

(3, 11) :

Minimum

Check critical point

(- \frac{1}{3}, \frac{13}{3}) :

Saddle

Minimum (3, 11), Saddle (- \frac{1}{3}, \frac{13}{3})

f (x) = 2 x^{3} + 45 x^{2} + 84 x + 29

x^{3} - 12 x^{2} + 36 x

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

x^{3} - 12 x + 2

f (x, y) = \frac{1}{3} y^{3} + x^{2} - 2 x y - 15 y + 12

What is the extreme f(x,y)=x^3+y^2-4xy+17x-10y+8 ?
The extreme f(x,y)=x^3+y^2-4xy+17x-10y+8 is Minimum(3,11),Saddle(-1/3 , 13/3)