- #1
Number2Pencil
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Homework Statement
Given the function
[tex]
f(x_1,x_2) = (x_1 - x_2^2)(x_1 - px_2^2)
[/tex]
where p is a constant parameter, for what value of p will the origin (0,0) be a singular point of this function?
Homework Equations
The Attempt at a Solution
I thought that singular meant either a discontinuity or shooting to infinity. I'm not really sure what to do here. I thought since singular point is related to curve smoothness and slope, I should take the gradient, and I got:
[tex]
\frac{\delta f}{\delta x_1} = 2x_1 - px_2^2 - x_2^2
[/tex]
[tex]
\frac{\delta f}{\delta x_2} = -2 x_2 (x_1-px_2^2) - 2(x_1 - x_2^2)p x_2
[/tex]
Where at the point (0,0), the value of p really makes no difference. Is my approach wrong?