Math Help - Cubic Hermite interpolation given some data

Time	Distance	Speed
0	0	75
3	225	77
5	383	80
8	623	74
13	993	72

Question: Use cubic Hermite interpolation to predict the position of the car and its speed when t = 10s.

My work

The last divided difference is


Now, I wrote the polynomial as


I evaluated this at t=10s but it came out to be around 77. If we plugged it into the previous polynomial, 77 would be too small.... even if it was speed, it looked wrong to me because the speed at t=10s is decreasing...

Hey jwxie.

You are mentioning two polynomials in your question but I can only see one which your Hermite approximation for the first three data points. Is there another polynomial you are comparing this Hermite one with?

Originally Posted by chiro

Hey jwxie.

You are mentioning two polynomials in your question but I can only see one which your Hermite approximation for the first three data points. Is there another polynomial you are comparing this Hermite one with?

I think the polynomial I wrote at the end was for the position. The f prime of that would be the speed...

but then again, if i plugged in 10 as x into the polynomial, the answer came out to be 77. If that was distance, it wouldn't make sense.... thanks!

Just out of curiosity, can you plot the polynomial and the data points belonging to your original sample?