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Re: Problem with conditional definitions


> I have recently uncovered a problem with conditional definitions of
> functions.  The following is a simple example
> 
> Remove[f]
> 
> f[x_ /; x <= 0] := x^2
> f[x_ /; 0 < x < 1] := x^3
> f[x_ /; x >= 1] := x^4
> 
> {f[1.], f'[1.],f''[1.]}
> 
> {1.,3.54208,18.8746}
> 
> Clearly incorrect. Or
> 
> {f[1.1],f'[1.1],f''[1.1]}
> 
>              {1.4641, 5.28974, 8.77428}
> Correct: {1.4641, 5.324,  14.52}
> 
> So it is not that the function was evaluated at a boundary.
> 
> Also, if I use exact arguments:
> 
> {f[1],f'[1],f''[1]}
> 
> {1,f'[1],f''[1]}
> 
> None of the function definitions lead to the answers I got. Did I miss
> something?
> --
> 
> Kevin J. McCann
> Johns Hopkins University APL

See

http://support.wolfram.com/Kernel/Symbols/System/Derivative.html

for notes about the limitations of automatic numerical differentiation.
Use ND (defined in the standard NumericalMath`NLimit` package to compute
derivatives of functions with sharp features.

Dave Withoff
Wolfram Research


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