What is the extreme x^2+y^2+6x-10y+5 ?

The extreme x^2+y^2+6x-10y+5 is Minimum(-3,5)

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extreme x^2+y^2+6x-10y+5

extreme points

x^{2} + y^{2} + 6 x - 10 y + 5

Minimum (- 3, 5)

Solution steps

Find the critical points:

(- 3, 5)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(- 3, 5) :

Minimum

Minimum (- 3, 5)

y = - 5 x^{3} + 4 x^{2} + 5 x - 1

f (x) = \frac{9 x ^{2} - 1}{x}

(x - 3) \cdot (x + 2) \cdot x

y = 5 + 12 x^{2} - 8 x^{3}

(x + 2) (x + 1) (x - 1) (x - 3)

What is the extreme x^2+y^2+6x-10y+5 ?
The extreme x^2+y^2+6x-10y+5 is Minimum(-3,5)