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

The extreme f(x,y)=4(x-y)-x^2-y^2 is Maximum(2,-2)

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extreme f(x,y)=4(x-y)-x^2-y^2

extreme points

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

Maximum (2, - 2)

Solution steps

Find the critical points:

(2, - 2)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(2, - 2) :

Maximum

Maximum (2, - 2)

\frac{3 x ^{2}}{x ^{2} - 25}

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

f (x) = - x^{2} + 12 x - 32

f (x) = 3 x^{2} - 12 x + 5, 0 \leq x \leq 3

f (x) = x - sin (x), 0 \leq x \leq 2 π

What is the extreme f(x,y)=4(x-y)-x^2-y^2 ?
The extreme f(x,y)=4(x-y)-x^2-y^2 is Maximum(2,-2)