If we were to keep them in SciPy, they might belong in scipy.optimize next to check_grad and approx_frime. But I don't think these functions (as written) are very useful. They have obvious computational inefficiencies and very limited functionality. I would rather point users to a fully functioning library for finite-differences like findiff: https://github.com/maroba/findiff

Thanks Stephan! I didn't hear about findiff before. Would you recommend it over https://github.com/pbrod/numdifftools?