What is the critical f(x,y)=x^3+3xy^2-6xy+1 ?

The critical f(x,y)=x^3+3xy^2-6xy+1 is (0,2),(0,0),(1,1),(-1,1)

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critical f(x,y)=x^3+3xy^2-6xy+1

critical points

f (x, y) = x^{3} + 3 x y^{2} - 6 x y + 1

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

Solution steps

x^{3} + 3 x y^{2} - 6 x y + 1

Find where

\nabla f (x, y)

is equal to zero or undefined

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

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

x^{2} + 6

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

f (x) = 2 x + \frac{128}{x}

f (x) = \frac{x ^{3}}{3} - 16 x

What is the critical f(x,y)=x^3+3xy^2-6xy+1 ?
The critical f(x,y)=x^3+3xy^2-6xy+1 is (0,2),(0,0),(1,1),(-1,1)