What is the critical 3x^3+xy^2-2xy+1 ?

The critical 3x^3+xy^2-2xy+1 is (0,2),(0,0),(1/3 ,1),(-1/3 ,1)

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critical 3x^3+xy^2-2xy+1

critical points

3 x^{3} + x y^{2} - 2 x y + 1

(0, 2), (0, 0), (\frac{1}{3}, 1), (- \frac{1}{3}, 1)

Solution steps

3 x^{3} + x y^{2} - 2 x y + 1

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 2), (0, 0), (\frac{1}{3}, 1), (- \frac{1}{3}, 1)

f (x) = 4 x^{3} - 9 x^{2} + 3 x + 1

3 x^{2} - 12 x

f (x) = x^{3} + 3 x^{2} - 45 x + 8

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

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

What is the critical 3x^3+xy^2-2xy+1 ?
The critical 3x^3+xy^2-2xy+1 is (0,2),(0,0),(1/3 ,1),(-1/3 ,1)