***Please using R for a), b), c). Please do not write, I want to see the coding, thank you!

***Please using R for a), b), c). Please do not write, I want to see the coding, thank you!

Let f(x, y) = 100(y x)2 + (1 x). This is the famed banana function (see wikipedia). The minimum of f is (1, 1) (why?). (a) Starting at the point (4, 4) use a fixed step size to locate the minimum. Here, since we are minimizing, your direction should be d(i) = -Vf(x(i)). How many iterations before you find the minimum? (This should take several tens of thousands of iterations.) (b) Starting at the point (4,4) use steepest descent with back- tracking to "find the minimum. How many iterations be- fore you find the mininum? (c) Use the R function nlm to find the minimum starting at (4,4). How many iterations? Compare to (a) and (b)