Let x be a function defined by

for x>0 f(x) = (|x-4|)/(x-2)

for x

5. (28 points) Let f be a function defined by lm-'ll f(a:)= mZ exsingm ifacSO W$>O whenever it is defined. (a) (2 points) Represent f as a case-defined function over its natural do main without using the absolute value function. (b) (8 points) Compute f' whenever it exists. When f is not differentiable at c e dom (f) indicate it and justify your claim.. You should decide whether you should apply differentiation rules or theorems. or use the definition of differentiability. (c) (5 points) Determine the critical points of f. (d) (3 points) Determine the intervals of increase as well as the intervals of decrease off, which are contained in (0,+oo). (e) (2 points) Show that f" has infinitely many zeros. (f) (8 points) Approximate f(3.2) by the quadratic Taylor polynomial of f at the reference point 7r. Further, find an upper bound for the absolute value committed. You may use the following formulas 8 sin $=$(1+3COSQ$+431112B) d3 1 and 838111213 2 ef'C (1 + 11003233 231112x) . (583 2