Re: new solution of an implicit function

Kaushik wrote:
hi, i was wondering if somebody could help me with this problem.
say i have an implicit function f:R x [0,1]-->R
f(x,a) =0 has a solution (x_0,a_0)

Assume that if we change a_0 slightly by a_1, such that |a_0-a_1|=c,
then there exists a new solution (x_1,a_1).

can anybody give some idea how to estimate |x_0-x_1| in terms of c and
any other suitable smoothness condition on f?

with suitable smoothness condition implicit function theorem says that
there is locally a function g such that g(x_0)=a_0, and if df/da at
a_0 is not zero then, g' is defined and is a continuous function. but
i'm looking for an estimate of |x_0-x_1|.

thanks
-kaushik

Not sure about second part. If x and a are dependent and independent
variables respy then using partial derivatives slope (dx/da)
= - f_a/ f_x = |x_0-x_1|/ |a_0-a_1|= |x_0-x_1|/ c

.

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