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

The critical f(x)=2x^2+axy+3y^2-2x+1 is (-(12)/(a^2-24),(2a)/(a^2-24))

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critical f(x)=2x^2+axy+3y^2-2x+1

critical points

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

(- \frac{12}{a ^{2} - 24}, \frac{2 a}{a ^{2} - 24})

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

(- \frac{12}{a ^{2} - 24}, \frac{2 a}{a ^{2} - 24})

y = x (x - 1)^{3}

f (x) = 6 y^{2} + 4 x^{2} - 12 x y - 4 y

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

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

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

What is the critical f(x)=2x^2+axy+3y^2-2x+1 ?
The critical f(x)=2x^2+axy+3y^2-2x+1 is (-(12)/(a^2-24),(2a)/(a^2-24))