A unique polynomial of degree _____________________ passes through n+1 data points
n+1
n
n or less
greater than n

Given the two points , the linear Lagrange polynomial  that passes through these two points is given by

The Lagrange polynomial that passes through 3 data points is given by

 The value of at x = 16 is

–0.07143l
-0.5000
0.57143
4.333

The following data of velocity of a body is given as a function of time.

A quadratic Lagrange interpolant is found using three data points, t=15, 18 and 22.  From this information, at what time is the velocity of the body 26 m/s during the time interval of t=15 to 22 seconds.

20.173 m/s
20.846 m/s
21.167 m/s
22.020 m/s

A robot is following a path on a x-y plane is found by interpolating four data points as

The length of the path from x = 2 to x = 7 is

The following data of the velocity of a body as a function of time is given 

 If you were going to use quadratic interpolation to find the value of the velocity at t=14.9 seconds, what three data points of time would you choose for interpolation?  Justify your answer.

0, 15, 18
15, 18, 22
0, 15, 22
0, 18, 24

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