Write a Matlab code which is able to implement the "Lagrange Interpolation Method for data set for any problem. Test your code for an engineering problem below.

"Submit a file which includes both your codeby using Lagrange Interpolation Method

A robot arm with a rapid laser scanner is doing a quick quality check on holes drilled in a ${15}^{\text{'}\text{'}}{10}^{\text{'}\text{'}}$ rectangular plate. The centers of the holes in the plate describe the path the arm needs to take, and the hole centers are located on a Cartesian coordinate system $($with the origin at the bottom left corner of the plate$)$ given by the specifications in the following table. Find the path traversed through the six points using a fifth order Lagrange polynomial. $($Use four digits after the decimal point$).$

$\backslash$table$[[$ in$),2\mathrm{.}00,4\mathrm{.}25,5\mathrm{.}25,7\mathrm{.}81,9\mathrm{.}20,10\mathrm{.}60],[$ in$),7\mathrm{.}2,7\mathrm{.}1,6\mathrm{.}0,5\mathrm{.}0,3\mathrm{.}5,5\mathrm{.}0]]$

Table. The coordinates of the holes on the plate.

If the laser is traversing from $x=2\mathrm{.}00$ to $x=4\mathrm{.}25$ to $x=5\mathrm{.}25$ like in a quadratic path, what is the value of $x=4\mathrm{.}00$ at using a fifth order Lagrange polynomial? Find the absolute relative approximate error for the fifth order polynomial approximation. Note: The absolute relative approximate error will be calculate by using the value $7\mathrm{.}1111$ obtained from the first order polynomial approximation.

$y$

Hint: For fifth order Lagrange polynomial interpolation $($also called quantic interpolation$),$ we choose the value of $y$ given by

$]=0[0$