# Is this a saddle?

by cambo86
 P: 25 For $$f(x,y)=x^2+y^3$$ Is there a saddle point at (0,0) or does the function have to have 2 or more sides going down like $$g(x,y)=x^2-y^2$$
 P: 1,538 Okay so have you taken the required derivative and found your critical points?
 P: 25 The critical point is (0,0). I'm just wondering if f(0,0) is a saddle point when the graph is shaped more like a chair than a saddle.
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Thanks
P: 25,228
Is this a saddle?

 Quote by cambo86 The critical point is (0,0). I'm just wondering if f(0,0) is a saddle point when the graph is shaped more like a chair than a saddle.
The exact shape doesn't matter. A saddle point is a stationary point that isn't a local max or min. Is yours?
P: 1,538
 Quote by cambo86 The critical point is (0,0). I'm just wondering if f(0,0) is a saddle point when the graph is shaped more like a chair than a saddle.
Are you familiar with the second derivative test? As in where you check :

$D = f_{xx}f_{yy} - f_{xy}^{2}$

This will allow you to see if your function has a saddle, min or max at a critical point ( Doesn't alwayyyyys work though ).
P: 25
 Quote by Dick The exact shape doesn't matter. A saddle point is a stationary point that isn't a local max or min. Is yours?
Yes, thank you.