What is the critical f(x,y)=sqrt(x^2+y^2-9)+sqrt(25-x^2-y^2) ?

The critical f(x,y)=sqrt(x^2+y^2-9)+sqrt(25-x^2-y^2) is (0,sqrt(17)),(0,-sqrt(17))

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critical f(x,y)=sqrt(x^2+y^2-9)+sqrt(25-x^2-y^2)

critical points

f (x, y) = x^{2} + y^{2} - 9 + 25 - x^{2} - y^{2}

(0, 17), (0, - 17)

Solution steps

x^{2} + y^{2} - 9 + 25 - x^{2} - y^{2}

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 17), (0, - 17)

f (x) = - x^{2} + 10 x - 21

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

x^{3} + y^{3} - 3 x y

f (x, y) = x y

f (x) = x^{4} - 4 x^{3} + 7

What is the critical f(x,y)=sqrt(x^2+y^2-9)+sqrt(25-x^2-y^2) ?
The critical f(x,y)=sqrt(x^2+y^2-9)+sqrt(25-x^2-y^2) is (0,sqrt(17)),(0,-sqrt(17))