Let approximating positive root of polynomial
f(x)=-1.4375-3.3x+2.675x^{2}+4.55x^{3}-4.5x^{4}+x^{5}
utilizing Newton's Method.
i) Use Newton algorithm to try to estimate root with tol=5\times 10^{-5} . Describe the results using initial guesses of 0.0, 1.0, 1.5, 2.0, 2.5, and 3.0;summarize the results in table(do not include all output generated).
ii) Can you determine the interval having positive root such that, if we begin with the initial guess in that interval, convergence will be guaranteed utilizing Newton's mehod?