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Parts of the first (I) and second (II) exams from Durrett, Spring 1998.I.2. Differentiate the following(a) 11 + 7x+ 5x3+3x2+ 2√x(b)x2+3x3+2x+4(c) (x3+ 3x)(x2+ 1)4(d)p1 +√2 + 3xI.3. Peekaboo Streak (the Winter Olympics were in 1998) is at the top of a ski jump. Weknow that her height as a function oftwill be a polynomialf(t) =a+bt+ct2+dt3+et4Use the following information to determine the constantsa,b,c,d, ande. (i) Her heightat timet= 0 is 70. (ii) Her velocity at timet= 0 is 0. (iii) Her acceleration at any timetis 16-t2.II.2. Sketch the graph of the following functionf(x) =x33-5x22+ 4xIndicate the set of values where it is (a) increasing, (b) convex (concave up).II.3.Bruno knows from his college daze that the functiong(x) =xlnxhas either amaximum or minimum at some pointx >0. Use the first derivative to find the locationof this point and the second derivative test to tell whether it is a minimum or maximum.