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

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

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

critical points

f (x) = 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})

y = x 4 - x

f (x, y) = - 2 x^{- 1} - x y + 128 y^{- 1}

x^{5}

f (x, y) = 2 x^{2} - 5 x y + 3 y^{4} + 5

f (x) = x + sin (2 x)

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