       Re: How to get the slope of a Interpolation[] function at a specified point?

• To: mathgroup at smc.vnet.net
• Subject: [mg26592] Re: How to get the slope of a Interpolation[] function at a specified point?
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 11 Jan 2001 10:39:07 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <93ee40\$dh@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

In[]:=geartable = {{0, 0}, {1, 1}, {2, 3}, {3, 4}, {4, 6}, {5, 7}, {6,
9.5}, {7,
12}, {8, 14}};
gearf = Interpolation[geartable, InterpolationOrder -> 6];

In[]:=gearf[4.5]

Out[]=6.40869

And here is the derivative :

In[]:=gearf'[4.5]

Out[]=0.85599

With  8 points you can't make a interpolation with order more than 8.

Regards
Jens

liwen liwen wrote:
>
> Dear Friends:
>              How are you!
>              I want to get the slope of a
> Interpolation[] function at a specified point,
> for example,here is a Interpolation function :
> geartable={{0,0},{1,1},{2,3},{3,4},{4,6},{5,7},{6,9.5},{7,12},{8,14}};
> Gear=Interpolation[geartable];
> y=Gear[4.5];
>
> I want to get the slope of Gear function at the point
> of {4.5,y},what should I do ?
> Can I use the FunctionInterpolation[] to make out a
> precise function to find the slope value ?
> Is the FunctionInterpolation[] precise enough to get
> the very precise slope value ?
>
> Best Regards,
>
> Liwen   E-mail:  gzgear at yahoo.com
>
> __________________________________________________
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> http://photos.yahoo.com/

```

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