> 3*x^2-2*x^3
> and
> 0.5*(1-cos(x*pi))
>
> practically lie on top of each other and have the same derivative.  I
guess
> that the sines are expressable as infinite series, but it's funny how it
> worked out.

Yeah, those are two extremely useful functions. The differences start coming
into play when you take the second derivative, I think.

Generally, I prefer the latter of the two, but I use the former in any case
where speed matters, since it can be calculated quickly by a computer when
written as:

x*x*(3-2*x)

This function is actually used in the POV-Ray source code to smooth out the
noise generator functions (bozo).

 - Slime
[ http://www.slimeland.com/ ]

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