numirical

The upward velocity of a rocket is given as a function of time in the table below: Answer the following: (a) Use Lagrange's formula or Newton's divided difference formula to find the quadratic polynomial P2(t) interpolating the given data. (b) Estimate the upward velocity of the rocket after 30 seconds using your answer to part (a) above. (c) Estimate the acceleration at t=15 seconds using the 2 nd order central difference formula. (d) Estimate the covered distance in the interval [10,20] seconds using all Simpson's Rules