Suppose that f(x, y, z) = x²yz - xyz³ is a function of three variables. 1. Find the gradient of f(x, y, z). Answer. Vf(x, y, z) 2. Evaluate the gradient at the point P(-1, -2,-2). Answer. Vf(-1, -2,-2) = = 3. Find the rate of change of f(x, y, z) at P in the direction of the vector u = Answer. Du f(-1, -2,-2) = = = (0, 1,-).

Suppose that f(x, y, z) = x²yz - xyz³ is a function of three variables. 1. Find the gradient of f(x, y, z). Answer. Vf(x, y, z) 2. Evaluate the gradient at the point P(-1, -2,-2). Answer. Vf(-1, -2,-2) = = 3. Find the rate of change of f(x, y, z) at P in the direction of the vector u = Answer. Du f(-1, -2,-2) = = = (0, 1,-).

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter2: Functions And Graphs

Section2.6: Proportion And Variation

Problem 22E: Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and...

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