A bowl has inner surface given by the graph of the function z = f(x, y) = 2x^2 + 3y^2. A drop of oil is placed on this surface at the point (2, 1, 11) and moves along the surface under the influence of gravity toward the point (0, 0, 0), with position function (x(t), y(t), z(t)). The projection into the xy-plane of its position is the pair (x(t),y(t)). Assume that gravity causes the drop to move so that the projection moves in the direction of the negative of the gradient vector of f. Find the curve in the xy-plane above which the drop moves. Give your answer in the form y = some function of x.

A bowl has inner surface given by the graph of the function z = f(x, y) = 2x^2 + 3y^2. A drop of oil is placed on this surface at the point (2, 1, 11) and moves along the surface under the influence of gravity toward the point (0, 0, 0), with position function (x(t), y(t), z(t)). The projection into the xy-plane of its position is the pair (x(t),y(t)). Assume that gravity causes the drop to move so that the projection moves in the direction of the negative of the gradient vector of f. Find the curve in the xy-plane above which the drop moves. Give your answer in the form y = some function of x.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 39RE

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