What is the extreme f(x,y)=x^2+y^2-2x+10y-15 ?

The extreme f(x,y)=x^2+y^2-2x+10y-15 is Minimum(1,-5)

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extreme f(x,y)=x^2+y^2-2x+10y-15

extreme points

f (x, y) = x^{2} + y^{2} - 2 x + 10 y - 15

Minimum (1, - 5)

Solution steps

Find the critical points:

(1, - 5)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(1, - 5) :

Minimum

Minimum (1, - 5)

f (x) = - x^{3} - x^{2} + 5 x - 4

f (x) = - x^{3} - x^{2} + 5 x - 5

f (x) = - x^{3} - x^{2} + 5 x - 3

- x^{2} + 10 x + 25

f (x) = 4 x^{3} - 440 x^{2} + 10500 x

What is the extreme f(x,y)=x^2+y^2-2x+10y-15 ?
The extreme f(x,y)=x^2+y^2-2x+10y-15 is Minimum(1,-5)