Use a Lagrange interpolating polynomial of the first and second order to evaluate the value of $y$ at $x=25$ based on the data in the following table;

$\backslash$table$[[x,10,30,50],[y,7\mathrm{.}7,1\mathrm{.}6,0\mathrm{.}424]]$

a$)$ Solve by hand by using first$-$order polynomial and the second$-$order polynomial

b$)$ Draw the flow chart expressing the algorithm for the solution.

c$)$ Create an $m-$script containing a function evaluating the $y-$values for the pre$-$defined $x-$values by means of Lagrange's Interpolation Method.

i$.$ Write the MATLAB Code $($m$-$script$)$ on the answer sheet.

ii$.$ Add explanation $($comment$)$ with $(\%)$ for each line of MATLAB Code.

iii. Build the $m-$script in MATLAB.

iv$.$ Run the $m-$script file and demonstrate the solution as screenshot using the "print screen" button on the keyboard.