What is the critical f(x,y)=x^2-y^2*sqrt(1-x^2-y^2) ?

The critical f(x,y)=x^2-y^2*sqrt(1-x^2-y^2) is (0,0),(0,-sqrt(2/3)),(0,sqrt(2/3))

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critical f(x,y)=x^2-y^2*sqrt(1-x^2-y^2)

critical points

f (x, y) = x^{2} - y^{2} \cdot 1 - x^{2} - y^{2}

(0, 0), (0, - \frac{2}{3}), (0, \frac{2}{3})

Solution steps

x^{2} - y^{2} 1 - x^{2} - y^{2}

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (0, - \frac{2}{3}), (0, \frac{2}{3})

What is the critical f(x,y)=x^2-y^2*sqrt(1-x^2-y^2) ?
The critical f(x,y)=x^2-y^2*sqrt(1-x^2-y^2) is (0,0),(0,-sqrt(2/3)),(0,sqrt(2/3))