ws22 - to form a cone. ²ind the magnitude of φ so that...

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WORKSHEET 22 - Fall 1995 1. The graph of the derivative of a function f ( x ) is given below. 13 4 2 f a) What are the critical points of f ( x )? b) Which critical point(s) correspond to relative extrema? Are they maxima or minima? c) Can you determine any inFection points? d) Graph f ( x ). 2. If f ( x )= ax 3 + bx 2 + cx + d , ±nd values for a , b , c ,and d so that f ( x ) has a local maximum at x = - 1, f ( - 1) = 2, and so that f ( x ) has a local minimum at x =1, f (1) = - 1. 3. a) ²ind the shortest line segment with endpoints on the x -and y -axes going through the point (1,8). b) What is the area of the triangle formed by the shortest line segment? c) What is the rate of change of area with respect to the x -coordinate of the point on the x -axis. d) ²or which x is the area increasing? 4. A garden is designed to be in the shape of a circular sector with radius R and angle θ .I fth ea r ea A is to be a constant, ±nd the dimensions ( R,θ ) which minimize the length of fence around the perimeter. θ R
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Unformatted text preview: to form a cone. ²ind the magnitude of φ so that the volume of the cone is maximized. 6. Twenty feet of wire are to be used to form two ±gures. In each of the following cases, how much should be used for each ±gure so that the total enclosed area is a maximum? a) equilateral triangle and square b) square and regular pentagon c) regular pentagon and hexagon d) regular hexagon and circle (Hint: The area of a regular polygon with n sides of length x is A = n 4 cot( π n ) x 2 .) What can you conclude from this pattern? 7. Two hallways meet at right angles. Their widths are a and b as indicated in the picture. What is the greatest length of a ladder which can be carried horizontally around the corner? a b 8. a) Find the closest point on the graph of f ( x ) = x 2 to the point ( a, b ). b) Show that the line connecting (0 , b ) to the closest point is normal to the graph at that point....
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This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.

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ws22 - to form a cone. ²ind the magnitude of φ so that...

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