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

http://i.imgur.com/WQWW6.png

The last divided difference is $\displaystyle \frac{-0.095 - (-0.0075)}{13-0} = -0.00673$

Now, I wrote the polynomial as $\displaystyle 75 + 0.8x - 0.0075x(x-3) - 0.00673x(x-3)(x-5)$

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...

Re: Cubic Hermite interpolation given some data

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?

Re: Cubic Hermite interpolation given some data

Quote:

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!

Re: Cubic Hermite interpolation given some data

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