[Caml-list] a small correction in OCaml tutorial Jason Hickey about second derivatives

[Caml-list] a small correction in OCaml tutorial Jason Hickey about second derivatives

[Robert Sherman]

Dear Reader,

In the book of Jason Hickey:
Introduction to Objective Caml
Section 3.1.3: Higher order functions, page 19 and 20
something regrettable is found:
The nice concept of Higher order function finds an
anti-apothesis under the remark that results of the second derivative 
function are "way off!"
Indeed, their values ought to be 6.0 and 60.0, but give both float 0.
Of course this should not be mentioned in a book, for this is not good 
for OCaml.
Jason Hickey gives an example like:  let f' = deriv f .... with 
differential dx = 1.0e-11
But is simply repairable, see here under:

While in Xavier Leroy et al.:
An introduction to OCaml
We find in Section 1.3 of page 15: let deriv f dx = ..... with 
differential dx = 1.0e-6
But they avoid the second derivative, what should not have worked much 
better.
However the cure is simply to prevent:
Just give dx a coarser value, even dx = 1.0e-5 comes with at least 4 
significant good digits
Using the definition of the second derivative should gain 1 or 2 digits.

Hope you will test these facts and make Jason Hickey a bit happier.

Robert Sherman
Zaandam
Pays Bas