In this question, you will sketch the graph of a continuous function f which has domain all real numbers except for :r: : 0, and satisfies all of the following properties: We also know: 1. f'(:c) and f\"(m) have the same domain as at) 2. f'(:c) = 0 only when a: = i2 and :I: = 7 3. We have f(7) : 215 but we do not give you the value of f(2) 4. f\"($) : 0 onlywhen :1: : 7, a: : 7 and :L' : 12 5. f(7) : 310 and recall that f(7) : 215 but we do not give you the value of f(12). The following is a table of the signs of the second derivative f\"(m )on the given intervals: m _- (a) (3 points for work on paper) Use this information to do the following. 0 Sketch the graph of a function f that satisfies all of these properties, with all mentioned m and 3; values labeled on the axes. 0 Label all critical points and local extrema. I Label all asymptotes and inflection points. (b) (4 points Mobius) Then answer the following FIVE questions. (i) Does f(:c) attain a global minimum ? 0 Yes O No Q Impossible to say (ii) Does f(:c) attain a global maximum ? 0 Yes O No Q Impossible to say (iii) How many inftection points are there on the graph of ns) ? 00 01 02 O3 O4ormore (iv) On what interval(s) is the graph of f concave up? Choose the best answer. (co, 7U) (012) of 00, no (0,7) 0( 7,0)u(12 oo) ou(0,7) (,712) O everywhere except m : 7, U, 12