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 $\displaystyle \frac{-0.095 - (-0.0075)}{13-0} = -0.00673$

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...