What is the extreme f(x,y)=sqrt(-25x^2+250x-y^2+8y-637) ?

The extreme f(x,y)=sqrt(-25x^2+250x-y^2+8y-637) is Maximum(5,4)

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extreme f(x,y)=sqrt(-25x^2+250x-y^2+8y-637)

extreme

Maximum (5, 4)

Solution steps

Find the critical points:

(5, 4)

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{25 x ^{2} - 250 x + 621}{( - 25 x ^{2} + 250 x - y ^{2} + 8 y - 637 ) - 25 x ^{2} + 250 x - y ^{2} + 8 y - 637}

D (x, y) = \frac{100}{( - y ^{2} - 637 - 25 x ^{2} + 250 x + 8 y ) ^{2}}

Check the sign of at each critical point

Check critical point

(5, 4) :

Maximum

Maximum (5, 4)

What is the extreme f(x,y)=sqrt(-25x^2+250x-y^2+8y-637) ?
The extreme f(x,y)=sqrt(-25x^2+250x-y^2+8y-637) is Maximum(5,4)