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

The extreme f(x,y)=-x^2-2y^2+xy+x+3y is Maximum(1,1)

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

extreme points

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

Maximum (1, 1)

Solution steps

Find the critical points:

(1, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 4

D (x, y) = 7

Check the sign of at each critical point

Check critical point

(1, 1) :

Maximum

Maximum (1, 1)

f (x) = - \frac{2}{3} x^{3} + 2 x^{2} + 6 x - 50

f (x) = x^{5} - 20 x^{4} + 8, 0 \leq x \leq 17

P (q, r) = 4 - q + r

\frac{d}{d x} (I n 1 - 2 x)

y = x^{2} - 12 x + 35

What is the extreme f(x,y)=-x^2-2y^2+xy+x+3y ?
The extreme f(x,y)=-x^2-2y^2+xy+x+3y is Maximum(1,1)