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Unformatted text preview: , 1), he is anxious to move in the direction in which the temperature drops the most rapidly. (a) Find the unit vector in the direction in which the temperature drops most rapidly at the instant he departs (5 , 1). (b) If the ant mistakenly moves toward the point (0 , 1), what rate of change will he experience at the instant he departs (5 , 1)? 6. (6 points) Let f ( x, y ) = 12 xy3 x 22 y 3 . (a) Find all the critical points of f . (b) For each critical point of f , determine whether f has a local maximum, local minimum, or saddle point at that point. 7. (8 points) Find the absolute maximum and absolute minimum values of f ( x, y ) = 2 xy + y 2 + 8 x4 y on the set D = { ( x, y )  ≤ x ≤ 2 , ≤ y ≤ 1 } 8. (6 points) Use Lagrange multipliers to ﬁnd the maximum and minimum values of f ( x, y ) = x 2 y subject to the constraint x 2 + y 2 = 1....
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This note was uploaded on 06/12/2008 for the course MATH 10C taught by Professor Hohnhold during the Spring '07 term at UCSD.
 Spring '07
 Hohnhold
 Math

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