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Given f(x, y, z) = x²y + y²z+z²x. (a) Find Vf(x, y, z). (b) Find the equation of the tangent plane to the surface f(x, y, z) = -1 at the (2, -1, 1). (c) Find the directional derivative of f(x, y, z) at the point (2, -1, 1) in the direction c point (5, 1, 7).

Given f(x, y, z) = x²y + y²z+z²x. (a) Find Vf(x, y, z). (b) Find the equation of the tangent plane to the surface f(x, y, z) = -1 at the (2, -1, 1). (c) Find the directional derivative of f(x, y, z) at the point (2, -1, 1) in the direction c point (5, 1, 7).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Given f(x, y, z) = x²y + y²z+z²x. (a) Find Vf(x, y, z). (b) Find the equation of the tangent plane to the surface f(x, y, z) = -1 at the point. (2,−1, 1). (c) Find the directional derivative of f(x, y, z) at the point (2, -1, 1) in the direction of the point (5, 1, 7).
Transcribed Image Text:Given f(x, y, z) = x²y + y²z+z²x. (a) Find Vf(x, y, z). (b) Find the equation of the tangent plane to the surface f(x, y, z) = -1 at the point. (2,−1, 1). (c) Find the directional derivative of f(x, y, z) at the point (2, -1, 1) in the direction of the point (5, 1, 7).
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