BUG: GH10365 in interpolate_1d when method is piecewise_polynomial
Starting point for closing #10365.
I only have the trivial case. I think this method (and perhaps other methods as well) needs #10383 for it to be useful. 

Added tests for `krogh` and `barycentric`.
 can you rebase
 Maybe I should just keep the tests for krogh and barbycentric? Piecewise polynomial needs higher order derivatives to be passed in for it to be useful -- otherwise it's just linear interpolation; not sure what a good way would be. 
 @kawochen what's the status of this?
 Still don't have a good way to pass in the higher order derivatives.  Will close if for now. 
