What is the critical f(x)=2x^3+xy^2+5x^2+y^2 ?

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

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critical f(x)=2x^3+xy^2+5x^2+y^2

critical points

f (x) = 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) = I n (2 - x)

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

f (x) = \frac{x ^{4} - 11 x ^{2} + 4}{( x ^{2} - 4 ) ^{2}}

x^{3} - x^{2} - 2 x

\frac{4}{( 1 - 4 x ^{2} ) ^{2}}

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