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)

Popular >

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

extreme points

f (x, y) = - 25 x^{2} + 250 x - y^{2} + 8 y - 637

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)

f (x, y) = 5 x^{2} y - 5 x y^{3} + 4 y^{3}

f (x) = 12 x - 6

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

f (x) = x + \frac{16}{x} + 6, 1 \leq x \leq 32

f (x) = 3 x^{2} - 4 x + 1, 0 \leq x \leq 2

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)