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

The extreme f(x,y)=2x^3+y^2-24x is Saddle(-2,0),Minimum(2,0)

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

extreme points

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

Saddle (- 2, 0), Minimum (2, 0)

Solution steps

Find the critical points:

(- 2, 0), (2, 0)

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

D (x, y) = 24 x

Check the sign of at each critical point

Check critical point

(- 2, 0) :

Saddle

Check critical point

(2, 0) :

Minimum

Saddle (- 2, 0), Minimum (2, 0)

What is the extreme f(x,y)=2x^3+y^2-24x ?
The extreme f(x,y)=2x^3+y^2-24x is Saddle(-2,0),Minimum(2,0)