Please use Julia pro to solve those question

Problem 3 (30%) a) Plot f(x) = - cos(10x); b) Use Hessian method to compute the minimum of f(x) in the interval of (-11, 1); c) Use any method from Julia for the minimization of f(x); d) Comment on rate to the minimum as a function of the initial point. If you choose the initial point randomly (uniform) in the (-11,1) interval, how often do you converge to the minimum? Problem 4 (40%) Using Rosenbrock function with a = 1 and b = 100; plot the distance of the kth iterate and the minimum, i.e., d(x(K), Xmin), using x0 = (-1,1) for the following methods: 1. Gradient descent; 2. Conjugate gradient; 3. Momentum; 4. Nesterov momentum; 5. Hyper Nesterov. For each method, show x(k) in a separate contour plot of the Rosenbrock function. [Hint: choose kmax = 100] SA X Ai Ae Pr Ps DO tv Problem 3 (30%) a) Plot f(x) = - cos(10x); b) Use Hessian method to compute the minimum of f(x) in the interval of (-11, 1); c) Use any method from Julia for the minimization of f(x); d) Comment on rate to the minimum as a function of the initial point. If you choose the initial point randomly (uniform) in the (-11,1) interval, how often do you converge to the minimum? Problem 4 (40%) Using Rosenbrock function with a = 1 and b = 100; plot the distance of the kth iterate and the minimum, i.e., d(x(K), Xmin), using x0 = (-1,1) for the following methods: 1. Gradient descent; 2. Conjugate gradient; 3. Momentum; 4. Nesterov momentum; 5. Hyper Nesterov. For each method, show x(k) in a separate contour plot of the Rosenbrock function. [Hint: choose kmax = 100] SA X Ai Ae Pr Ps DO tv