1. (35 points) Implement a simpler version of your newton Matlab function that allows for an array of initial guesses to be input and runs for a set number of iterations without checking for convergence or collecting residual va Your function should have the following inputs and output Inputs . a function () . The derivative f(r) an array of initial guesses ro . A maximum mumber of iterations N Outputs IN" The .Vrs iterate array of newton, regardless of convergence. The first line of your code should read function x-nevton simple(f,df,x0,N) 2. (35 points) Implement a Matlab function that creates a Newton basin image with the following inputs and outputs: Inputs CEc The coordinates of a polynomial r) . oz-[r1 ''2rni '722] the limits of the plane h r2?? [imi ?mg] of inital values in the .ng-n .N- A maximum number of newton iterations. complex plane. the number of grid points in the rcal and imaginary direction, respoc- tively Outputs . An image of ord(p)+1 colors, where each color corresponds to a different converged root, and black corresponds to no root being found. While you may use any color mapping you like (for example, the hsv, built-in color array) to correspond to the different roots, plcase use black to denote that no root was Sound. Put the polynomial in the title of the image. (Use a tolerance of 10to check convergence) The first line of your code should read function neuton basin(c,ax,ng,N)