What is the extreme f(x,y)=3-sqrt(25-(x+1)^2-(y-1)^2) ?

The extreme f(x,y)=3-sqrt(25-(x+1)^2-(y-1)^2) is Minimum(-1,1)

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extreme f(x,y)=3-sqrt(25-(x+1)^2-(y-1)^2)

extreme points

f (x, y) = 3 - 25 - (x + 1)^{2} - (y - 1)^{2}

Minimum (- 1, 1)

Solution steps

Find the critical points:

(- 1, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{x ^{2} + 2 x - 24}{( - x ^{2} - 2 x + 2 y + 23 - y ^{2} ) - x ^{2} - 2 x + 2 y + 23 - y ^{2}}

D (x, y) = \frac{25}{( - x ^{2} - y ^{2} + 23 - 2 x + 2 y ) ^{2}}

Check the sign of at each critical point

Check critical point

(- 1, 1) :

Minimum

Minimum (- 1, 1)

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

f (x) = ln (2 + sin (x))

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

f (x y) = 2 x^{2} - 8 x + y^{2} + 16 y + 100

g (x) = 2 x^{3} + 3 x^{2} + 12 x - 4

What is the extreme f(x,y)=3-sqrt(25-(x+1)^2-(y-1)^2) ?
The extreme f(x,y)=3-sqrt(25-(x+1)^2-(y-1)^2) is Minimum(-1,1)