the conceptual problems I won't need help with as much, I'm trying to learn Matlab right now so what would be really helpful is the programming part of this in matlab. I understand it's really specific but a thumbs up to anything that helps me with the programming at all!

(2) (Root finding and Optimization) (Programming) (a) Suppose f(x) is differentiable on [a, b]. Discuss how you might use a rootfinding method to identify a local extremum of f(x) inside [a, b]. (b) Let /(x) = log2 - sina. Prove that f(x) has a unique maximum in the interval [4,6]. (Note that log means natural logarithm.) (c) Approximate this local maximum using 12 iterations of the enclosure methods (Bi- section and False Position) with starting interval (4,6). You should code these two methods yourself. (d) What is your best estimate for p, the location of the maximum? (e) Compare the two algorithms using the following two tables. Table 1: Approximation Pr versus iteration number n Iteration n Bisection False Position Table 2: Absolute errorP-pl versus iteration number n Iteration n Bisection False Position (1) Plot the log of the absolute error for the two methods on the same graph. (g) Don't forget to turn in your code