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

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

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

critical points

f (x) = 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) = x^{2} - 3 y^{2} - 8 x + 9 y + 3 x y

x^{3} + 9 x^{2} + 24 x + 1

f (x) = x^{3} - x^{2} - 6 x

(x - 2) e^{x}

f (x) = x (12 - x)^{3}

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