1. In what situation does Newton's method converge only linearly?
2. Explain the role that round off errors play in the convergence of solvers for nonlinear equations, and explain their relationship with convergence errors.
3. State a similarity and a difference between the problem of minimizing a function φ(x) and that of solving the nonlinear equation φ'(x) = 0.
4. State what a convex function is, and explain what happens if an objective function is convex.