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, 1, –1). Answer: Vƒ(−1, 1, -1) =□ 3. Find the rate of change of f(x, y, z) at P in the direction of the vector u = (0, 1/1 , - /³/1). Answer: Du f(-1, 1, −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, 1, –1). Answer: Vƒ(−1, 1, -1) =□ 3. Find the rate of change of f(x, y, z) at P in the direction of the vector u = (0, 1/1 , - /³/1). Answer: Du f(-1, 1, −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 18E
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Transcribed Image Text: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, 1, –1).
Answer: Vƒ(−1, 1, -1) =□
3. Find the rate of change of f(x, y, z) at P in the
direction of the vector u = (0, 1/1 , - / ).
Answer: Du f(-1, 1, −1) =
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