Answer please with R code if possible

Question 2 (a simple optimization) Consider a minimization problem with two arguments (the Rosenbrock function): f(x1,T2) = (1-x1)2 + 100 (x22 a. Write an R function that takes a vector (of two elements) as the input and output the Rosenbrock function value b. Finally, use the optim) function to find and report the minimizer. c. (bonus) Write your own R code of coordinate descent algorithm to obtain the minimal solution. You can choose either Gauss-Seidel or Jacobi implementation