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OP In x'(t) = 3t^2 + 2
x'(t) means the first derivative of x with resepct to t.
That is, the rate at which x changes as t changes.
x''(t) would be the second derivative.
x'''(t) would be the third.
The caret symbolizes exponentiation which is difficult to represent on a computer otherwise. In mathematica, it might be possible to do it. I'm not sure. Old versions of basic used "**", so one would write x'(t) = 3*t**2 + 2 where one asterisk denoted multiplication and two exponentiation.
As that page was not written for a program, but for a human to read, he left out the single asterisk, because most people would understand that better.
Smoothing in relation to functions means trying to come up with parameters that make a function more "natural" looking. There's an art to it, as well as a science. We had to do splines in graduate numerical analysis, which is trying to find a smooth curve to fit n points. I haven't used it since, but I'm vaguely aware that they use splines in some kinds of graphics applications.
Smoothing over age and time should be a property of a function that gets smoother as t increases.
Entire Thread Subject Posted By Posted Mild derivative amusement. TheFallibleFiend 01/20/06 02:32 PM Re: Mild derivative amusement. TEd Remington 01/20/06 03:30 PM Re: Mild derivative amusement. Jackie 01/20/06 03:45 PM Re: Mild derivative amusement. TheFallibleFiend 01/20/06 04:34 PM Re: Mild derivative amusement. Buffalo Shrdlu 01/20/06 04:48 PM
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