# Having some trouble. Estimate the slope of the tangent line.

• January 20th 2011, 01:24 AM
qleeq
Having some trouble. Estimate the slope of the tangent line.
I've been given a table of values and I have to estimate the instantaneous velocity at t = 2002. I can do this by averaging two secant lines, but it wants me to measure the slope of the tangent. Here's the table.

t | N
1996 | 44
1998 | 69
2000 | 109
2002 | 141
2004 | 182
2006 | 233

I really have no idea where to start.
• January 20th 2011, 02:47 AM
DrSteve
Here is one way to get a rough approximation:

$f'(2002)$ is approximately $\frac{f(2004)-f(2002)}{2004-2002}$.