141Bquiz6c - y = 0 the back wall x = 0 and the ²oor z = 0...

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1 MATH 141B Quiz#6 Due: Tues March 4, 2008 [ 2 ] 1. Find the maximum value of the function f ( x, y ) = 9 - 2 x + 4 y - x 2 - 4 y 2 . A) z = 3, B) z = 5, C) z = 10, D) z = 11, E) none of the above [ 2 ] 2. For the function f ( x, y ) = x 4 + y 4 - 4 xy + 1, which of the following 3 statements are true? i) f has exactly one local maximum. ii) f has exactly one local minimum. iii) f has exactly one saddle point. A) ii) only, B) i) and ii) only, C) i) and iii) only, D) iii) only, E) none true [ 2 ] 3. Find the volume of the largest rectangular box in the ±rst octant with 3 faces of the box lying in the coordinate planes (i.e., the side wall
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Unformatted text preview: y = 0, the back wall x = 0, and the ²oor z = 0) and one vertex lying on the plane x + 2 y + 3 z = 6 . A) 1, B) 4 / 3, C) 2, D) 7 / 3, E) none of the above [ 2 ] 4. If f ′′ ( x ) = e 2 x , f (0) = 4 and f ′ (0) = 2 , then ±nd f (1 / 2) . A) e + 1, B) e/ 2, C) e 2 + 1 4 , D) e + 2, E) none of the above [ 2 ] 5. Solve the initial value problem b xy ′ + y = x sin x y ( π/ 2) = 0 and compute y ( π ) . A) 1-1 π , B) 1 + 1 π , C) 1-π 2 , D) 1 + π 2 , E) none of the above...
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This note was uploaded on 03/30/2008 for the course MATH 141B taught by Professor Marcfabbri during the Spring '08 term at Penn State.

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