MATH 131 Midterm: MATH131 BOYLE-M SPRING2016 ALL-SECTION EXAM2

• School: University of Maryland
• Department: Mathematics
• Course: MATH 131
• Professor: All

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From a class of ten students, a team of 3 students will be chosen. What is the number of possible teams? (b) (5pts. ) Ten people remain in competition at an olympic event. Find every critical point of f . (b) (10 pts. ) At each critical point, determine whether f has a local maxi- mum, local minimum or saddle point. 3. (chemotaxis) suppose a bacterium nds food by moving toward the highest concentration of glucose. Suppose it starts at the point ( 2, 1) in the xy-plane, and the concentration of glucose, in certain units, is f (x, y) = 3 + x2 + y2 (a) (3 pts. ) Draw the level curve of f which contains ( 2, 1). (b) (7 pts. ) Find the direction in which the bacterium will move initially. (c) (2 pts. ) What is dz/dt when t = 0: (a) (8 pts. )