What is the critical 2x^3+9xy^2+15x^2+27y^2 ?

The critical 2x^3+9xy^2+15x^2+27y^2 is (0,0),(-5,0),(-3,2),(-3,-2)

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critical 2x^3+9xy^2+15x^2+27y^2

critical points

2 x^{3} + 9 x y^{2} + 15 x^{2} + 27 y^{2}

(0, 0), (- 5, 0), (- 3, 2), (- 3, - 2)

Solution steps

2 x^{3} + 9 x y^{2} + 15 x^{2} + 27 y^{2}

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (- 5, 0), (- 3, 2), (- 3, - 2)

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

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

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

f (x) = \frac{1}{4} x^{4} - \frac{1}{3} x^{3} - 6 x^{2}

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

What is the critical 2x^3+9xy^2+15x^2+27y^2 ?
The critical 2x^3+9xy^2+15x^2+27y^2 is (0,0),(-5,0),(-3,2),(-3,-2)