Math 1351 011 Exam II B Makeup October 20 2006 Answer the problems on separate paper You do not need to rewrite the problem statements on your answer sheets Do your own work Show all relevant steps which lead to your solutions Attach this question sheet to the front of your answer sheets 1 6pts Using the definition find the derivative of f x 2 x 2 3 x 2 40pts Using the rules of differentiation find the derivative of each of the following functions Simply the results where appropriate Write the final form of each of the derivatives using positive exponents only 3x 2 x2 4x a a x 6 x 4 4 x 4 12 x5 b b x c c x 5 xe 5 x e 5 x 5 d d x sin 1 x 2 sin 2 x e e x ln x 2 2 x 5 3 8pts Let f x x 2 sin 2 x Find and simplify f x 4 8pts Let f x 2 x x 4 5 8pts Let s t 1 10t 2t 2 1 t 5 describe the position of a moving object Find x 5 Find the equation of the tangent line to the graph of y f x at a where the object is advancing b where the object is retreating c the total distance the body travels 6 8pts A person standing at the top of a tower throws a rock straight up It is observed that 2 seconds after the person releases the rock that it reaches its maximum height and 6 seconds later it strikes the ground at the base of the tower Find a b c d 7 8pts a What was the initial velocity of the rock What was the initial height of the rock when it was released from the person s hand What was the maximum height which the rock reached during its flight What was the velocity of the rock when it struck the ground Find y for the following implicitly defined function x 2 3 xy y 3 10 8 8pts Find the equation of the tangent line to the curve defined by 2 x 2 y 2 4 y 1 at the point 1 3 9 8pts An traffic accident victim is being airlifted in a helicopter from Seymour which is 150 miles due east of Lubbock to Lubbock The helicopter departs Seymour at 1 00 pm Because of weather conditions the helicopter is flying at 60 mph The victim s parents are driving in a car from Midland which is 80 miles due south of Lubbock to Lubbock They depart Midland at 2 00 pm They are driving at a rate of 50 mph At 3 00 pm the helicopter and the car are the same distance from Lubbock At 3 00 pm how fast is the distance between the helicopter and the car decreasing
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