You will need to use MATLAB or Python to answer parts (a) and (b) of this question. Fiona, Brian and James are interested in the function f(I) = 5 + 12 sin (6r) for I E [1, 2]. (a) [2 marks] Brian asks you to use the MATLAB function fzero or the Python function brentq from scipy . optimize to find the smallest root of f on the interval [1, 2]. Fiona reminds you to plot the function in MATLAB or Python first to find a suitable starting value. smallest root = 1.04734 Give your answer to at least 6 significant figures. You may need to change the display format in MATLAB. (b) [2 marks] James wants you to look for the root closest to 1.5 by implementing your own Newton's method with the starting value 21 = 1.5. You obtain the iterates: 1.572008 1.567726 Give your answers to at least 6 significant figures. (c) [1 mark] Fiona reminds you to check the general convergence theory for Newton's method. Which of the following is correct for this method? If fe C?([1, 2]) and the starting point In is sufficiently close to a simple root in (1, 2), then this iterative method converges quadratically. O If fe C?([1, 2]) and the starting points I, and zy are sufficiently close to a simple root in (1, 2), then this iterative method converges superlinearly with order v == 1.6. O If fe C([1, 2]) and f(1)f(2)