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

The critical f(x)=x^3+2y^2+2xy-5 is (0,0),(1/3 ,-1/6)

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

critical points

f (x) = x^{3} + 2 y^{2} + 2 x y - 5

(0, 0), (\frac{1}{3}, - \frac{1}{6})

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (\frac{1}{3}, - \frac{1}{6})

y = x 8 - x^{2}

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

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

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

f (x) = 2 x^{3} + 5 x^{2} - x + 1

What is the critical f(x)=x^3+2y^2+2xy-5 ?
The critical f(x)=x^3+2y^2+2xy-5 is (0,0),(1/3 ,-1/6)