What is the extreme f(x,y)=x^2+y^2-2x+14y-11 ?

The extreme f(x,y)=x^2+y^2-2x+14y-11 is Minimum(1,-7)

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extreme f(x,y)=x^2+y^2-2x+14y-11

extreme points

f (x, y) = x^{2} + y^{2} - 2 x + 14 y - 11

Minimum (1, - 7)

Solution steps

Find the critical points:

(1, - 7)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(1, - 7) :

Minimum

Minimum (1, - 7)

f (x) = - 3 x^{2} + 30 x - 4

\frac{9 e ^{x}}{1 + e ^{- x}}

f (x) = 81 x - 3 x^{3}

F (x, y) = y^{2} - x^{2}

f (x, y) = - 6 x^{2} - 3 x y - 3 y^{2} - 69 x - 9 y + 7

What is the extreme f(x,y)=x^2+y^2-2x+14y-11 ?
The extreme f(x,y)=x^2+y^2-2x+14y-11 is Minimum(1,-7)