What is the extreme f(x,y)=2x^2+3xy+4y^2+2x-10y ?

The extreme f(x,y)=2x^2+3xy+4y^2+2x-10y is Minimum(-2,2)

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extreme f(x,y)=2x^2+3xy+4y^2+2x-10y

extreme points

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} + 2 x - 10 y

Minimum (- 2, 2)

Solution steps

Find the critical points:

(- 2, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 8

D (x, y) = 23

Check the sign of at each critical point

Check critical point

(- 2, 2) :

Minimum

Minimum (- 2, 2)

\frac{1}{2 x + 3}

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

f (x) = x e^{- 6 x}, 0 \leq x \leq 2

f (x) = x^{6} (x - 4)^{5}

P (q, s) = q + 8 + s

What is the extreme f(x,y)=2x^2+3xy+4y^2+2x-10y ?
The extreme f(x,y)=2x^2+3xy+4y^2+2x-10y is Minimum(-2,2)