What is the extreme f(x,y)=x^3+9x^2+y^2+24x+2y+17 ?

The extreme f(x,y)=x^3+9x^2+y^2+24x+2y+17 is Minimum(-2,-1),Saddle(-4,-1)

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extreme f(x,y)=x^3+9x^2+y^2+24x+2y+17

extreme points

f (x, y) = x^{3} + 9 x^{2} + y^{2} + 24 x + 2 y + 17

Minimum (- 2, - 1), Saddle (- 4, - 1)

Solution steps

Find the critical points:

(- 2, - 1), (- 4, - 1)

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

D (x, y) = 2 (6 x + 18)

Check the sign of at each critical point

Check critical point

(- 2, - 1) :

Minimum

Check critical point

(- 4, - 1) :

Saddle

Minimum (- 2, - 1), Saddle (- 4, - 1)

f (x) = \frac{2 x - 5}{x + 6}

2^{x^{2} - 5}

f (x) = x^{\frac{3}{4}} - 4 x^{\frac{1}{4}}

x = \frac{2}{x}

f (x) = 420 - x x

What is the extreme f(x,y)=x^3+9x^2+y^2+24x+2y+17 ?
The extreme f(x,y)=x^3+9x^2+y^2+24x+2y+17 is Minimum(-2,-1),Saddle(-4,-1)