Problem $1.($Module $6)5$ points

The measured velocity of a moving object is recorded in Table $1.$ It is desired to estimate the

velocity at $t=15$ seconds between the last two data points.

a$)$ Find the Lagrange interpolating polynomial $P(t)$ in standard form that smoothly

connect all $5$ points.

b$)$ Find the interpolated value at $t=15$ using interpolating polynomial you found in a$).$

Note: the Matlab program for Example #$4,$ Module $6$ can be used for this problem

Table $1$

Matlab script $($do not include lagran.m function$)($use $10$pt font size$)$

Put your answer in this box:

$$ Interpolating polynomial, P$($t$)=$

$$ Interpolated value at t $=15,$ P$(15)=$