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

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

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

critical points

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

(- 1, 1), (1, 1)

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

(- 1, 1), (1, 1)

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

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

\frac{x}{x - 1}

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

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