Numerical Methods: 3 Point Formula

AI Thread Summary
The discussion revolves around using the 3-point formula to approximate the first derivative of a function in a Numerical Methods course. The user successfully applied the formula to the first three points but encountered difficulty with the fourth point due to the lack of subsequent values. A suggestion was made to apply the same method used for the first point, implying that a negative step size could be utilized. This approach raises questions about the validity of using negative increments in derivative approximations. The conversation highlights the challenges of numerical methods when boundary conditions limit available data points.
bobmerhebi
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Hello there,

I am taking a Numerical Methods course & i had a lecture today when we did an example on the 3-point formula to approximate the 1st derivative of f.

the example included 4 given x's with their images by f. & we had to get all the images for the 1st derivative of f.

so we used one of the two 3-point formulas to get the values for f' for each of the first 3 x's. the last x was left without an attempt to get its f'(x).

So tonight i was wondering about how could I apply the formula to get it & its seems that I can't, after all either of the 3 point formula's requires the values of either the previous & following x or the two values following x. In either cases that's not possible as there's is no value after this particular x.

my question is whether there's some kind of solution to this & if so or not how so ?

P.S. this is Not a HW question but rather a help in my lecture.

Thank you
 
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To estimate f' for the 4th point, can't you use the same method as the 1st point? In other words, can't h be negative?
 
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