4. Give an example of each of the following. If no such example exists, then explain why not. Your example should be an appropriately labeled graph. (a) A function f and an initial guess Il such that Newton's method fails to converge to a zero of f using 21. (b) A continuous function that has no absolute extrema, but does have both one local maximum and one local minimum. Explicitly state the domain of your function. (c) A discontinuous function that achieves both an absolute maximum and absolute minimum on (-6,-4). (d) A function f defined on (-3,3] with no absolute minimum, one local minimum, an absolute maximum, no local maximum, and two critical numbers.