ASM 24.18-19, Clamped Splines

[jthomps7]

So as I was doing the practice problems for ASM Lesson 24, I came across these two multiple choice problems. I thought I had gotten both correct, but both were wrong.

The solutions say that for a clamped spline, the first derivative of the spline is equal to the first derivative of the original function at both endpoints.

I saw no mention of this in the reading. I thought that the first derivative at each endpoint merely needed to be set equal to some specified value (usually given).

Can anyone shed some light on this?

[MyKenk]

IIRC, for a clamped spline, the first derivative at the endpoints is equal to some number, usually an approximation based on what you want the 'tails' of your spline to do. However, when you are fitting a spline to a function, you have a general idea what the function (and the underlying data) is doing at the endpoints. Since the function has a derivative (assumedly) at the endpoints, and you are fitting another function (the spline) to it, you may as well use the actual derivatives, rather than some arbitrary approximation.

It might NOT be in the reading, but it makes sense. let me know if I can explain better. As you stated, "the first derivative at each endpoint merely needed to be set equal to some specified value." In this case, it's not given, but assumed that, since you are fitting to a function, you use the underlying function.