Computing3?25 using MATLAB.
(a) Beginning with the interval [2,3], and f(x) =x^3?25, use theerror bound for bisection to predict how many iterates bisectionwould need to get error within 10^?20.
(b) Run bisection on this problem. How many iterations did itneed? For some of the iterates compute the absolute error. What ishappening approximately to the number of significant digits ofaccuracy with each iteration?
(c) Write a program to perform Newton’s method on f(x) =x^3?25with p0= 3 to get an approximation to 3?25 that is accurate towithin 10^?20. Calculate the derivative by hand and hard code it inas a new function. How many iterates did it need? Save all of theiterates.
(d) Compute the absolute error and the number of significantdigits of accuracy for each iterate. What is happening to thenumber of significant digits with each iteration? Compare tobisection
