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

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

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

critical points

f (x, y) = 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})

+ 3 (x - 3)^{2} - 1

f (x) = x^{3} + 6 x^{2} + 9 x + 3

f (x) = x^{3} + 4 x^{2} + 4 x - 6

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

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

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