x^2+2xy+3y^2 - Wolfram|Alpha

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Input

x^2 + 2 x y + 3 y^2

Geometric figure

elliptic paraboloid

Roots

y = -1/3 i (sqrt(2) x - i x)

y = 1/3 i (sqrt(2) x + i x)

Polynomial discriminant

Δ_x = -8 y^2

Partial derivatives

d/dx(x^2 + 2 x y + 3 y^2) = 2 (x + y)

d/dy(x^2 + 2 x y + 3 y^2) = 2 (x + 3 y)

Indefinite integral

integral(x^2 + 2 x y + 3 y^2) dx = x^3/3 + x^2 y + 3 x y^2 + constant

Global minimum

$min{x^2 + 2 x y + 3 y^2} = 0 at (x, y) = (0, 0)$

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