What is the extreme f(x,y)=9x^2+y^2 ?

The extreme f(x,y)=9x^2+y^2 is Minimum(0,0)

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extreme f(x,y)=9x^2+y^2

extreme points

f (x, y) = 9 x^{2} + y^{2}

Minimum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = 36

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Minimum (0, 0)

f (x) = \frac{x ^{3}}{3} - x^{2} - 15 x

f (x, y) = x^{2} - x y + y^{2} + 9 x - 6 y + 10

f (x, y) = x^{2} y + y^{3} - 48 y

f (x) = - 5 x^{4} - 5 x^{3} + 29

f (x) = 7 sin (x) + 7 cos (x), 0 \leq x \leq 2 π

What is the extreme f(x,y)=9x^2+y^2 ?
The extreme f(x,y)=9x^2+y^2 is Minimum(0,0)