  We consider the problem of numerically identifying roots of a target function
- under the constraint that we can only measure the derivatives of the function
at a given point, not the function itself. We describe and characterize two
methods for doing this: (1) a local-inversion "inching process", where we use
local measurements to repeatedly identify approximately how far we need to move
to drop the target function by the initial value over N, an input parameter,
and (2) an approximate Newton's method, where we estimate the current function
value at a given iteration via estimation of the integral of the function's
derivative, using N samples. When applicable, both methods converge
algebraically with N, with the power of convergence increasing with the number
of derivatives applied in the analysis.
