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) =

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

See similar textbooks