[oceanofsolaris]

Not to sound too snobby (I would have notrecognized the Newton-Raphson method is by its name either), but I think it is at least plausible to figure out the method on the spot.

If you either know how the first order of a Taylor series looks like or just brainstorm a bit about how the derivative could help you in finding a root, you will figure out the Newton-Raphson method rather quickly. But then, it really depends on the job whether this is actually knowledge the interviewer would want to test.

That said, I completely understand that even if you would have the required knowledge, it is really easy to fumble during a high-stress situation.