What is the critical f(x,y)=ax^2+2xy+3y^2+4x-1 ?

The critical f(x,y)=ax^2+2xy+3y^2+4x-1 is (-6/(-1+3a), 2/(-1+3a))

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critical f(x,y)=ax^2+2xy+3y^2+4x-1

critical points

f (x, y) = a x^{2} + 2 x y + 3 y^{2} + 4 x - 1

(- \frac{6}{- 1 + 3 a}, \frac{2}{- 1 + 3 a})

Solution steps

a x^{2} + 2 x y + 3 y^{2} + 4 x - 1

Find where

\nabla f (x, y)

is equal to zero or undefined

(- \frac{6}{- 1 + 3 a}, \frac{2}{- 1 + 3 a})

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

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

2 cos (t) + sin (2 t)

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

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

What is the critical f(x,y)=ax^2+2xy+3y^2+4x-1 ?
The critical f(x,y)=ax^2+2xy+3y^2+4x-1 is (-6/(-1+3a), 2/(-1+3a))