Performance improvements and obtaining the points that define the linearization

[SouthEndMusic]

I really like the premise of this package, and would like to use it in the context of linear programming. I do however see that there is some low hanging fruit when it comes to performance improvements, in the form of reducing allocations and resolving type instabilities.

Also, I would like to be able to obtain the points that define the piecewise linear approximation, I haven't found functionality within the package to do that directly.

I'd be happy to open a PR myself for this, would there be anyone available to review it?

[SouthEndMusic]

@gdalle would it be easy for you to introduce DI in this package? Or maybe it would be better to be able to optionally provide your own derivative functions, which default to ForwardDiff.

[gdalle]

I don't think this package would benefit very much from derivative flexibility, because it only manipulates scalar quantities. One thing where DI would help is to replace the one (artificial) use of Hessian with its optimized version of second_derivative with the ForwardDiff backend.