What is the extreme f(x,y)=-x^2-5y^2+8x-10y ?

The extreme f(x,y)=-x^2-5y^2+8x-10y is Maximum(4,-1)

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extreme f(x,y)=-x^2-5y^2+8x-10y

extreme points

f (x, y) = - x^{2} - 5 y^{2} + 8 x - 10 y

Maximum (4, - 1)

Solution steps

Find the critical points:

(4, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 10

D (x, y) = 20

Check the sign of at each critical point

Check critical point

(4, - 1) :

Maximum

Maximum (4, - 1)

What is the extreme f(x,y)=-x^2-5y^2+8x-10y ?
The extreme f(x,y)=-x^2-5y^2+8x-10y is Maximum(4,-1)