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September 15th, 2012, 03:40 PM   #1
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Estimating derivative from table of values

If a function has the set of points (1000,32); (2000,33); (3000,46); (3500, 55); (3600,61); (3800,65); (4000,69); (5000,70), the problem is to estimate the derivative at the point (3500,55). Which would be the best method of estimating, averaging the slopes of the two secants from x=3000 to x=3500 and x=3500 to x=4000 (the x values are both 500 away from the point in question)? Or averaging the slopes of the two secants from x=3000 to x=3500 and x=3500 to x=3600 (the two x values closest to the point in question)? There are definitely other ways to estimate the derivative but between those two averaging methods which would be the best? In summary, is it better to average two secant slopes of equal distance from the point in question or average the two secant slopes of the closest points to the point in question? Thanks a lot.
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September 15th, 2012, 03:43 PM   #2
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Re: Estimating derivative from table of values

I'm personally favoring the method where the other two chosen x values are evenly spaced (3000 and 4000).
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