What is the critical 2x^3+xy^2+5x^2+y^2 ?

The critical 2x^3+xy^2+5x^2+y^2 is (0,0),(-5/3 ,0),(-1,2),(-1,-2)

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critical 2x^3+xy^2+5x^2+y^2

critical points

2 x^{3} + x y^{2} + 5 x^{2} + y^{2}

(0, 0), (- \frac{5}{3}, 0), (- 1, 2), (- 1, - 2)

Solution steps

2 x^{3} + x y^{2} + 5 x^{2} + y^{2}

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (- \frac{5}{3}, 0), (- 1, 2), (- 1, - 2)

f (x, y) = \frac{1}{3} x^{3} + y^{3} + 2 x^{2} - 12 x - 3 y

f (x, y) = 4 x^{2} - 12 x + y^{2} + 2 y - 10

\frac{x}{( x - 1 ) ^{2}}

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

y = - \frac{cos ( 2 x )}{2} - 2 sin (x)

What is the critical 2x^3+xy^2+5x^2+y^2 ?
The critical 2x^3+xy^2+5x^2+y^2 is (0,0),(-5/3 ,0),(-1,2),(-1,-2)