What is the critical f(x,y)=10+2x^4-8x^2+4xy-y^2 ?

The critical f(x,y)=10+2x^4-8x^2+4xy-y^2 is (0,0),(-1,-2),(1,2)

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critical f(x,y)=10+2x^4-8x^2+4xy-y^2

critical points

f (x, y) = 10 + 2 x^{4} - 8 x^{2} + 4 x y - y^{2}

(0, 0), (- 1, - 2), (1, 2)

Solution steps

10 + 2 x^{4} - 8 x^{2} + 4 x y - y^{2}

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (- 1, - 2), (1, 2)

f (x) = x^{\frac{1}{3}} (2 x^{2} - 8)

f (x) = - x^{2} + 14 x

f (x) = cos (\frac{π x}{2})

3 x^{5} + 5 x^{3}

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

What is the critical f(x,y)=10+2x^4-8x^2+4xy-y^2 ?
The critical f(x,y)=10+2x^4-8x^2+4xy-y^2 is (0,0),(-1,-2),(1,2)