What is the extreme f(x,y)=x^2-2x+y^2-6y+30 ?

The extreme f(x,y)=x^2-2x+y^2-6y+30 is Minimum(1,3)

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extreme f(x,y)=x^2-2x+y^2-6y+30

extreme points

f (x, y) = x^{2} - 2 x + y^{2} - 6 y + 30

Minimum (1, 3)

Solution steps

Find the critical points:

(1, 3)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(1, 3) :

Minimum

Minimum (1, 3)

f (x, y) = e^{y l n (x)}

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

f (x) = 2 x - 3, 0 \leq x \leq 2

f (x, y) = \frac{x ^{2}}{4} + y^{2}

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

What is the extreme f(x,y)=x^2-2x+y^2-6y+30 ?
The extreme f(x,y)=x^2-2x+y^2-6y+30 is Minimum(1,3)