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?
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?