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MathGroup Archive 2001

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26641] Re: How to get the slope of a Interpolation[] function at a specified point?
  • From: "Paul Lutus" <nospam at nosite.com>
  • Date: Sat, 13 Jan 2001 22:36:17 -0500 (EST)
  • References: <93ee40$dh@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

If you want the slope of a function, take its derivative.

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

In[12]:=f[4.5]
Out[12]=6.46875
In[13]:=f'[4.5]
Out[13]=0.895833

And definitely look at this:

Plot[{f[x],f'[x]},{x,0,8}]

Remember that the meaning of the slope depends entirely on the interpolation
method, since the original data are fixed data points.

--
Paul Lutus
www.arachnoid.com


"liwen liwen" <gzgear at yahoo.com> wrote in message
news:93ee40$dh at smc.vnet.net...
> 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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