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Let f(x, y) = 10-3r² +4. (a) Find the gradient Vƒ(2,-3) of f at the point P(2,−3). (b) Find the directional derivative D₁ƒ(2,-3) of ƒ in the direction of the vector =(,1). (c) Find the largest and smallest directional derivative of f at the point P, as well as the directions in which they occur.

Let f(x, y) = 10-3r² +4. (a) Find the gradient Vƒ(2,-3) of f at the point P(2,−3). (b) Find the directional derivative D₁ƒ(2,-3) of ƒ in the direction of the vector =(,1). (c) Find the largest and smallest directional derivative of f at the point P, as well as the directions in which they occur.

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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Let f(x, y) = 10 - 3x² + 4. (a) Find the gradient Vƒ(2, -3) of f at the point P(2,-3). (b) Find the directional derivative D₁ƒ(2,-3) of f in the direction of the vector =(³, 1). u= (c) Find the largest and smallest directional derivative of f at the point P, as well as the directions in which they occur.
Transcribed Image Text:Let f(x, y) = 10 - 3x² + 4. (a) Find the gradient Vƒ(2, -3) of f at the point P(2,-3). (b) Find the directional derivative D₁ƒ(2,-3) of f in the direction of the vector =(³, 1). u= (c) Find the largest and smallest directional derivative of f at the point P, as well as the directions in which they occur.
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