What is the extreme P(x,y)=-4x+5y-x^2+2xy-7y^2+9 ?

The extreme P(x,y)=-4x+5y-x^2+2xy-7y^2+9 is Maximum(-23/12 , 1/12)

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extreme P(x,y)=-4x+5y-x^2+2xy-7y^2+9

extreme points

P (x, y) = - 4 x + 5 y - x^{2} + 2 x y - 7 y^{2} + 9

Maximum (- \frac{23}{12}, \frac{1}{12})

Solution steps

Find the critical points:

(- \frac{23}{12}, \frac{1}{12})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 14

D (x, y) = 24

Check the sign of at each critical point

Check critical point

(- \frac{23}{12}, \frac{1}{12}) :

Maximum

Maximum (- \frac{23}{12}, \frac{1}{12})

f (x) = 2 x^{2} + 5 (7 - x)^{2}

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

f (x) = - 3 csc (x)

f (x) = \frac{x ^{3}}{3} - 375 x^{2} + 129600 x

f (x) = e^{4 x - x^{2}}

What is the extreme P(x,y)=-4x+5y-x^2+2xy-7y^2+9 ?
The extreme P(x,y)=-4x+5y-x^2+2xy-7y^2+9 is Maximum(-23/12 , 1/12)