Suppose you have the solution to the following problem
$$ (1) \ \text{minimize} f(x) \\ \text{subject to} \ Ax = b$$
How do you determine the maximum $\epsilon$ such that the solution to (2)
$$ (2) \ \text{minimize} f(x) \\ \text{subject to} \ Ax = b+\epsilon$$
can be accurately written in terms of the solution of (1) using a Taylor series expansion?