What is the critical f(x,y)=sqrt(9-(\sqrt{x^2+y^2)-4)^2} ?

The critical f(x,y)=sqrt(9-(\sqrt{x^2+y^2)-4)^2} is (0,4),(0,-4)

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critical f(x,y)=sqrt(9-(\sqrt{x^2+y^2)-4)^2}

critical points

f (x, y) = 9 - (x^{2} + y^{2} - 4)^{2}

(0, 4), (0, - 4)

Solution steps

9 - (x^{2} + y^{2} - 4)^{2}

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 4), (0, - 4)

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

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

f (x) = - \frac{cos ( 2 x )}{2} - 2 sin (x)

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

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

What is the critical f(x,y)=sqrt(9-(\sqrt{x^2+y^2)-4)^2} ?
The critical f(x,y)=sqrt(9-(\sqrt{x^2+y^2)-4)^2} is (0,4),(0,-4)