# Finding the derivative of a set of points

• Sep 29th 2010, 03:22 PM
YaoPau
Finding the derivative of a set of points
I have a dataset of thousands of values arranged in one column. Over time, those values create a curve that resembles, say, a sine curve, moving up to a peak, down to a bottom point, and moving back up again.

Given the set of numbers, I want a formula that tells me the slope of the curve at that point. For example, if the six most recent points in the set are 44.9, 50.0, 53.0, 53.1, 50.0, 49.1 I want the formula to show that 49.1 is decreasing from the peak with a slight negative slope. Further, if the next six points are 47.5, 41.6, 35.4, 23.6, 11.5, -2.0, I want to show that -2.0 is around halfway between the peak and the bottom with a large negative slope.

How can I do this in calculus to get more accurate results than just taking the slope of the last few numbers?
• Sep 29th 2010, 03:57 PM
pickslides
Quote:

Originally Posted by YaoPau

How can I do this in calculus to get more accurate results than just taking the slope of the last few numbers?

If you had a function that models this data you can get an approximation of the slope at these points.
• Sep 29th 2010, 04:10 PM
YaoPau
The curve isn't uniform like a sine curve. I guess the best example I could give is how the stock market fluctuates somewhat randomly but often rises to peaks and descends to valleys.

In other words, is there a way to find a derivative for a set of points that don't belong to a function?
• Sep 29th 2010, 04:18 PM
pickslides
Because your points are at discrete intervals you will have to take the gradient between the points with the normal rise over run method.

You can approximate the gradient at a point by using the rise over run method using the the previous point and the point after that. Although I can't see this being very accuarate.