write Matlab code please 4. Consider finding the root of the function f(x) = x + 4x

write Matlab code please

 

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4. Consider finding the root of the function f(x) = x + 4x (a) Use your Newton's method function with initial guess x1=1.5, tol- erance 10-10, and a max number of steps 20. Print a table that includes the iteration number n, the value of an at each iteration, and the error at each iteration En = n - n-1. Note: The error for cannot be computed. In order to make E the same size as a for your table, you can fill in E = 0 for the first error. (b) Use the following four fixed point iteration functions g(x) with your code from Problem 3 to approximate the root of the function f using an initial guess of x1 = 1.5, a tolerance of 10-10, and a max number of steps of 20. Print a table for each gi(x) that includes the iteration number n, the value of xn at each iteration, and the error at each iteration En|xn - n-1|- = i. 9(x) = ii. 92(x) = x- - iii. 93(x) = 10 4+x x+4x-10 3x +8x 10-23 4 10 V iv. 94(x) = x + 4x + x - 10 and En using your an- En En En-1' E-1 En- Show how these fixed point iterations find the roots of f(x) (take f(x) and rearrange it into g. (x) or take g(x) and rearrange it into f(x) for all i. You can do this by hand and submit a second pdf or type it in the text of your Matlab pdf). (c) Make a table with the ratios swer from part a and b (There should be 5 tables). What do these ratios tell us about each fixed point iteration g(x)? Why might this be? What does it tell you about Newton's method for this function? Do you notice anything between 92(x) and your Newton's method results? 6 4. Consider finding the root of the function f(x) = x + 4x (a) Use your Newton's method function with initial guess x1=1.5, tol- erance 10-10, and a max number of steps 20. Print a table that includes the iteration number n, the value of an at each iteration, and the error at each iteration En = n - n-1. Note: The error for cannot be computed. In order to make E the same size as a for your table, you can fill in E = 0 for the first error. (b) Use the following four fixed point iteration functions g(x) with your code from Problem 3 to approximate the root of the function f using an initial guess of x1 = 1.5, a tolerance of 10-10, and a max number of steps of 20. Print a table for each gi(x) that includes the iteration number n, the value of xn at each iteration, and the error at each iteration En|xn - n-1|- = i. 9(x) = ii. 92(x) = x- - iii. 93(x) = 10 4+x x+4x-10 3x +8x 10-23 4 10 V iv. 94(x) = x + 4x + x - 10 and En using your an- En En En-1' E-1 En- Show how these fixed point iterations find the roots of f(x) (take f(x) and rearrange it into g. (x) or take g(x) and rearrange it into f(x) for all i. You can do this by hand and submit a second pdf or type it in the text of your Matlab pdf). (c) Make a table with the ratios swer from part a and b (There should be 5 tables). What do these ratios tell us about each fixed point iteration g(x)? Why might this be? What does it tell you about Newton's method for this function? Do you notice anything between 92(x) and your Newton's method results? 6