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 > > > > __________________________________________________ > Do You Yahoo!? > Yahoo! Photos - Share your holiday photos online! > http://photos.yahoo.com/ >