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Unformatted text preview: MATH 2163, Calculus.III Exam 2 (20 pts.) Suppose you are standing on the surface z = 2x 3 + xy2 + 5x 2 + y2 at the point (-2, I) and z gives the elevation of the surface above the xy-plane. Answer each part by showing your work or explaining how you got your answer. Name: j ,.' -- ;/ f ;/ f a 2 f a 2 f I, . (15 pts.) Calculate and simplify the following expression- 2 +-- +-- +- 2 for ax axay ayax ay f(x.y) = 4x 3 y'_ 3xy- 5x 2 + sy'. /2 . a, In what direction in the xy-plane from (-2, I) should you proceed if you wish your elevation to increase the fastest? b, If you move in the direction of Part (a) above, what will be your rate of change for fin this direction? c. In what direction from (-2, I) should you proceed if you want your elevation to stay the same? d. Suppose instead you decide to go from the point (-2, I) to the point (-5, 5), Is your / _~ation increasing or decreasing at the moment you move in this direction and at what J rate?...
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- Spring '08
- Calculus, pts, The Tangent, closed rectangular box