What is the extreme f(x)=x^2+y^2+6x-18y ?

The extreme f(x)=x^2+y^2+6x-18y is Minimum(-3,9)

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extreme f(x)=x^2+y^2+6x-18y

extreme points

f (x) = x^{2} + y^{2} + 6 x - 18 y

Minimum (- 3, 9)

Solution steps

Find the critical points:

(- 3, 9)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(- 3, 9) :

Minimum

Minimum (- 3, 9)

f (x) = (x - 9)^{2}

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

f (x, y) = 3 x y - 6 x - y^{2}

f (x) = \frac{8}{x ^{2} + 1}

f (2.52, 5.15) = 3 x^{4} y^{2} - 18 x y

What is the extreme f(x)=x^2+y^2+6x-18y ?
The extreme f(x)=x^2+y^2+6x-18y is Minimum(-3,9)