3. Condition Number. We saw in class that a fixed step size is able to guarantee linear convergence. The choice of step size we gave in class, however, depended on the function f. Show that it is not possible to choose a fixed step size t, that gives convergence for any strongly convex function. That is, for any fixed step size t, show that there exists (by finding one!) a smooth (twice continuously-differentiable) strongly convex function with bounded Hessian, such that a fixed-stepsize gradient algorithm starting from some point x0, does not converge to the optimal solution. 3. Condition Number. We saw in class that a fixed step size is able to guarantee linear convergence. The choice of step size we gave in class, however, depended on the function f. Show that it is not possible to choose a fixed step size t, that gives convergence for any strongly convex function. That is, for any fixed step size t, show that there exists (by finding one!) a smooth (twice continuously-differentiable) strongly convex function with bounded Hessian, such that a fixed-stepsize gradient algorithm starting from some point x0, does not converge to the optimal solution