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220Exam1B - down(iii At what points on the graph are there...

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Math 220, Elementary Calculus: Professor Patrick Fitzpatrick Teaching Assistants: Rodrigo Trevino and Sauleh Siddiqui First Exam (Version B), Oct 6 , 2009 Write your name, your TA’s name, the number of your discussion section and VERSION B on each answer sheet. Begin each problem on a new answer sheet. Show your work. You may not use notes, books, calculators, cell phones or any other electronic devices during the exam. 1. (20 points) Find the derivative, f 0 ( x ) , of each of the following functions: ( i ) f ( x ) = 1 + 2 x + 1 /x ( ii ) f ( x ) = x + 1 /x 2 ( iii ) f ( x ) = (5 x + 1) 3 ( iv ) f ( x ) = 1 / (1 + x 2 ) 2. (20 points) (i) Find the equation of the tangent line to the graph of the function f ( x ) = x 2 at the point on the graph at which x = 3 . (ii) At what point on the graph is the tangent line parallel to the line y=10x+3? 3. (20 points) Graph the function f ( x ) = 2 x 3 - 3 x 2 - 12 x + 1 . (i) State explicitely the intervals on which it is increasing and decreasing. (ii) State explicitly the intervals on which it is concave up and concave
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Unformatted text preview: down. (iii) At what points on the graph are there local maximum, local minimum and points of inection? 4. (20 points) A rectangular storage shed with a square base is to be built. The material for the oor costs $5 per square foot, the material for the roof costs $3 per square foot and the material for the sides costs $2 per square foot. Find the dimensions of the shed that has 250 cubic feet of volume and minimizes the cost of the material for construction. State explicitly and label the Objective Function (5 points). State explicitly and label the Constraint Equation (5 points). 5. (20 points) A ball is thrown into the air and its distance s ( t ) from the ground t seconds later is given by s ( t ) = 5 + 96 t-16 t 2 . (i) What is the initial velocity of the ball? (ii) At what time does the ball reach its maximum height? What is the maximum height? 1...
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