Question: Consider the simple equation f (x) = x 3 x 2 . Do the following analysis for this equation: (a) Determine the three roots

Consider the simple equation f (x) = x³ − x². Do the following analysis for this equation:

(a) Determine the three roots by hand.

(b) Perform the first five iterations by hand for Picard’s method for an initial guess of 0.1.

(c) Write a MATLAB program to compute the solution by Picard’s method. How many iterations are required to get to within 0.01 of the nearest root for an initial guess of 0.1?

(d) How many iterations of Newton’s method are required to reach the same level of accuracy? You should do this by hand and by a MATLAB program.

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