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?