Exam II-D of Math 1351-011: Derivatives and Tangent Lines, Exams of Mathematics

Download Exam II-D of Math 1351-011: Derivatives and Tangent Lines and more Exams Mathematics in PDF only on Docsity! Math 1351-011 Exam II-D October 18, 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 .2( ) 3 7f x x 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. a. b.5 44 5 12( ) 6 4a x x x x = − − + 2 3 2( ) 4 xb x x x − = + c. d.5 5( ) 5 5x xc x xe e− −= − − + 1 2 2( ) sin sind x x x−= − e. 2( ) ln 2e x x x= − 3. (8pts) Let . Find (and simplify) .2( ) cos 2f x x x= ( )f x′′ 4. (8pts) Let . Find the equation of the tangent line to the graph of at( ) 7 4f x x x= + − ( )y f x= .2x = 5. (8pts) Let describe the position of a moving object. Find:2( ) 1 10 2 , 1 5 ,s t t t t= + − ≤ ≤ 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 7 seconds later it strikes the ground at the base of the tower. Find: a. What was the initial velocity of the rock? b. What was the initial height of the rock when it was released from the person’s hand? c. What was the maximum height which the rock reached during its flight? d. What was the velocity of the rock when it struck the ground? 7. (8pts) Find for the following implicitly defined function:y′ a. 3 34 12x xy y− − =