Given the first three approximations for a root of a continuous function /(*): x0,X,x2> Muller's method will take the next one, JC3, to be that solution in Exercise 9 that is closest to x2 (the most current approximation). It then continues the process, replacing JC0, xu JC2 by JC,, χ2>*3 t 0 construct the next approximation, x4 . (a) Show that the latter formula in Exercise 9 is less susceptible to floating point errors than the first one. (b) Write an M-file, call it muller, that will perform Muller's method to find a root. The syntax should be the same as that of the secan t program in Exercise for the Reader except that this one will need three initial approximations in the input rather than 2. (c) Run your program through six iterations using the function f(x) = JC4 – 2 and initial approximations x0 = l,x, = 1.5,JC2 =1.25 and compare the results and errors with the corresponding ones in where the secant method was used.
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