Environmental Application of Interpolation and Optimization AlgorithmsIn this assignment we will use interpolation and optimization algorithms to analyze heat transfer inan environmentalapplication. Lakes in temperate climates can become thermally stratified during the summer: a layer of warm buoyantwater near the surface, called the epilimnion, overlies a layer of colder denser water near the bottom, called thehypolimnion. The thermocline is a thin horizontal layer that separates the epilimnion and hypolimnion. Quantifyingthermal stratification in lakes, in particular estimating the depth of the thermocline, can be important whenmodelling the impacts of pollution. Using data which describe the temperature TCz(inm),we will approximate the depth of thermocline in Michigan's Platte Lake ?(()()()1).The following data represent measurements of the temperature at various depths on Platte Lake:Question 1. Newton Interpolation of Temperature DataBuild a MATLAB function" [f]=newtoninterpolation (p,q)" which takes n data points (x1,y1),dots,(xn,yn)asinput variables, and outputs a polynomial interpolant f=f(x)of degree n-1,by following Newton's divideddifference algorithm. Then, use your MATLAB function to produce a polynomial interpolant TNewton(z) which fitsthe provided data from Platte Lake. Use MATLAB to produce a plot of your polynomial interpolant TNewton(z) overthe interval of depths zin[1,26].Question 2. Estimating the Depth of the ThermoclineFor the purpose of this assignment, we will define the depth of the thermocline zthermoclineas2 :z=zthermoclineis the depth z where the magnitude of thederivative |T'(z)|is maximized over the interval zin[1,26]0,27.223to approximate the depth of thethermocline zthermoclinein[1,26] according to the polynomial interpolant TNewton(z) you obtained in Question 1.Inother words, find the depth z=zthermocline where |TNewton'(z)|is maximized on the interval 1,26. Use an errorbound of err =10-2in your approximation.