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Math 121 Final - Final Exam MATH 121 Fall 2006 Name_Section...

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Page 1 of 10 Final Exam MATH 121 Fall, 2006 Name________________________________________________Section____________ Show all your work on the exam paper, legibly and in detail, to receive full credit. No Calculators. 1. (10 points) Find an equation of the tangent line to the curve xy y x 3 3 3 = + at the point 2 3 , 2 3 .
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Page 2 of 10 2. (4 points each) Find dx dy . Note: You do not need to simplify your answers. a) ( ) x xe y = 1 ln b) 2 5 x e y = c) ( ) x y 3 sin 1 = d) = 2 3 4 cos ln x x y
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Page 3 of 10 e) ( ) x e x e y 3 = f) x x y 1 2 tan = g) x e y x ln = h) x x y sin =
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Page 4 of 10 3. (5 points each) Find the limit. a) ( ) x x x 3 1 lim + b) x x x 1 sin 1 lim 0
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Page 5 of 10 4. (10 points) Find: (a) the intervals on which f is increasing, (b) the intervals on which f is decreasing, (c) the open intervals on which f is concave up, (d) the open intervals on which f is concave down. ( ) 27 36 3 2 2 3 + = x x x x f
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Page 6 of 10 5. (10 points) Sketch the graph of ( ) x f . Your graph should reflect the regions where ( ) x f is increasing and decreasing, and where
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