find the root(s) of the following functions using both Newton's method and the secant method, using tol = eps.

3 Find the root s of the following functions using both Newton's ulethod and the anat inethod using tol epa. . You will vood to experiment with the parameters po, pl, ad maxits. . For each root, visualize the iteration history of both methods by plotting the albsolute errors, as a function . Label the two curves (Newton's method and secaut method) using a legend, desacribing the po and p (a) f:z2, which has two roots, z2 of itcrution mumbser, on a (single) semilogy plot values you used, eg, "Newton's (po 7)" and Secant (po-0, pl 1)" Rewrite the iteration formula to verify it is the saine as the Babylonian method (see worksheet Q1 (a)). Explsin the problem with the starting guess po " 0 in terims of the derivative of f. (b) f:z tanb(r), which has oue root, r 0 Characterixe (rouglhly) wbeu the methods converge or diverge in terms of the starting xuesses, (E g. try Newtou's metbod with po -1.08 aud 1.09.) (c) fi-2r +2, which has oue root, z 1.769- (d) f: z + +, wlich has cine root,0. (la Matlab, use nthroot (x,3) mausul of x"(1/3).) (e) (Challeng; unograded f: What happens with Newtou's method wheu po 0 or 17 duewhich has a root at r 0. Can you find the root? (Explain what you olsxerve:) Nobe that t