Auxiliary functions

> pts := (x,y) -> zip((x,y)->[x,y], x, y):

> dd := proc(x,y)
local k;
[seq((y[k]-y[k-1])/(x[k]-x[k-1]),
k=2.. min(nops(x),nops(y)))]
end:

> cd := proc(x,y)
local k;
[seq((y[k]-y[k-2])/(x[k]-x[k-1])/2,
k=3.. min(nops(x),nops(y)))]
end:

> hd := proc(x,y)
local k;
[seq(
(y[k-2]-8*y[k-1]+8*y[k+1]-y[k+2])/(x[k]-x[k-1])/12,
k=3.. min(nops(x),nops(y))-2)]
end:

> with(stats):
with(describe):

> with(plots):