Odd behavior of InterpolationFunction derivative

• To: mathgroup at smc.vnet.net
• Subject: [mg29368] Odd behavior of InterpolationFunction derivative
• From: Tomas Garza <tgarza01 at prodigy.net.mx>
• Date: Fri, 15 Jun 2001 02:23:38 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```"Interpolation[data] constructs an InterpolatingFunction object which
represents an approximate function that interpolates the data. The data
can have the forms {{x1, f1},{x2, f2},...} or {f1, f2,...}, where in the
second case, the xi are taken to have values 1, 2, ..." (on-line Help
Browser). The following example shows that while in both cases the
InterpolationFunction works properly, the first derivatives appear to be
different. Take, for example, Sin[x] in the range (-Pi/2, Pi/2), and
construct a list of 11 values thereof in order to obtain an
interpolation function.

In[1]:=
points = Table[x, {x, -Pi/2, Pi/2, Pi/10}];
vals = Table[Sin[x], {x, -Pi/2, Pi/2, Pi/10}];

In[3]:=
functionOne = Interpolation[Transpose[{points, vals}]];
functionTwo = Interpolation[vals];

In[5]:=
Plot[{functionOne[x], (functionOne[#] &)'[x]}, {x, -Pi/2, Pi/2}];

In[6]:=
Plot[{functionTwo[x], (functionTwo[#] &)'[x]}, {x, 1, 11}];

In both plots the graph of the approximation of Sin[x] appears
correctly. However, in the second plot the graph of the interpolated
derivative, Cos[x], is clearly wrong.

What is going on? Is this a bug (aka "feature")?

Tomas Garza
Mexico City

```

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