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Unformatted text preview: Polytechnic Institute of NYU MA 1024/1324 Worksheet 12 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 Total 100 1 2 (1) Find the global maximum and global minimum of f . (a) f ( x ) = x + 1 x 2 , x ∈ [1 , √ 2] (b) f ( x ) = sin 2 x √ 3 cos x , 0 ≤ x ≤ π . 3 (2) Find the global maximum and global minimum of f ( x ) = 2 2 x x 2 , 2 ≤ x ≤  x 2  , < x < 3 1 3 ( x 2) 3 , 3 ≤ x ≤ 4 4 (3) Find the maximum and minimum values of y by implicit differentiation. 2 x 2 4 xy + 3 y 2 8 x + 8 y 1 = 0 5 (4) An electric current, when flowing in a circular coil of radius r , exerts a force F = kx ( x 2 + r 2 ) 5 / 2 on a small magnet located at a distance x above the center of the coil. Find the distance above the center of the coil where the force on the magnet is greatest. 6 (5) Find the minimum distance from the point (4 , 2) to the parabola y 2 = 8 x . 7...
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This note was uploaded on 12/09/2009 for the course MA 1024/1324 taught by Professor N/a during the Spring '09 term at NYU Poly.
 Spring '09
 N/A
 Calculus

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