What is the extreme f(x,y)=50+2x+3y-3x^2-y^2-0.5xy ?

The extreme f(x,y)=50+2x+3y-3x^2-y^2-0.5xy is Maximum(0.21276…,1.44680…)

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extreme f(x,y)=50+2x+3y-3x^2-y^2-0.5xy

extreme points

f (x, y) = 50 + 2 x + 3 y - 3 x^{2} - y^{2} - 0.5 x y

Maximum (0.21276 \dots, 1.44680 \dots)

Solution steps

Find the critical points:

(0.21276 \dots, 1.44680 \dots)

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

D (x, y) = 11.75

Check the sign of at each critical point

Check critical point

(0.21276 \dots, 1.44680 \dots) :

Maximum

Maximum (0.21276 \dots, 1.44680 \dots)

U (x, y) = - x^{2} - 3 y^{2} + 2 x y + 100 x

f (x) = x^{2} + \frac{120}{x}

f (x, y) = \frac{1}{2} y^{4} - 4 x y + 2 x^{4}

f (x) = 2 x^{5} ln (x)

f (x) = 48 x^{3} + 57 x^{2} - 54 x + 18

What is the extreme f(x,y)=50+2x+3y-3x^2-y^2-0.5xy ?
The extreme f(x,y)=50+2x+3y-3x^2-y^2-0.5xy is Maximum(0.21276…,1.44680…)