I'm completely lost with matrix differentiation.

So I'm really kinda bummed out because I just don't get how to solve numerical differentiation problems with linear algebra. As an example :

Estimate f ' (-1) if f (1) = 3, f (0) = -2, f (-2) = -18.

I'd like to say I have an idea on how to at least set up the problem, but to be honest I have no idea. I would think we to use the transpose of the vandermond matrix like we would in numerical integration. But I'm not positive.

Sorry, I know I'm essentially asking you to guide me through step by step from the beginning, but I don't know what else to do as I've read the section in my textbook multiple times and I'm still lost.