What is the critical f(x)=x^3+y^3+3x^2-3y^2-8 ?

The critical f(x)=x^3+y^3+3x^2-3y^2-8 is (0,2),(0,0),(-2,2),(-2,0)

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critical f(x)=x^3+y^3+3x^2-3y^2-8

critical points

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

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

Solution steps

x^{3} + y^{3} + 3 x^{2} - 3 y^{2} - 8

Find where

\nabla f (x, y)

is equal to zero or undefined

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

x^{3} + 6 x^{2} - 15 x

2 x^{\frac{5}{3}} - 5 x^{\frac{4}{3}}

y = \frac{x ^{2}}{x ^{2} + 3}

f (x) = 2 x^{3} - 6 x^{2} - 18 x + 2

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

What is the critical f(x)=x^3+y^3+3x^2-3y^2-8 ?
The critical f(x)=x^3+y^3+3x^2-3y^2-8 is (0,2),(0,0),(-2,2),(-2,0)