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

• To: mathgroup at smc.vnet.net
• Subject: [mg26589] How to get the slope of a Interpolation[] function at a specified point?
• From: liwen liwen <gzgear at yahoo.com>
• Date: Tue, 9 Jan 2001 01:52:03 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```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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```

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