a.) Consider the function: f(:r) = log(;r)/;r2. We wish to nd a root for the equation f(:L') = 0. Can we be sure that Newton's method will converge when we start from any point in the domain of f? b.) Consider the following optimization problem: minimize an, x2) = log(:r1;r2) + 22% + 332 + 3(zr1332)4 Can we be sure that the Gradient Search procedure to minimize f would converge? If so, would it converge to a local minimum or global minimum? c.) Consider the following optimization problem: minimize f[:r1,;r2) : (.171 1)2 + (3:2 2)2 If we start with an initial point (0,0) would Newton's method converge faster, slower, or at the same rate as the gradient method given that we use line search for both methods? Why