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Question 2. Let f(x, y) = 5xy² + sin(x + y). Find the following: (a) The gradient of f(x, y). (b) The gradient of the function f at the point (π, π). (c) The directional derivative of the function f at the point (7, 7) in the direction of the vector (3, 4). (d) The maximum rate of change of the function f at the point (7,0). (e) The direction in which the function f decreases fastest at the point (7,0).

Question 2. Let f(x, y) = 5xy² + sin(x + y). Find the following: (a) The gradient of f(x, y). (b) The gradient of the function f at the point (π, π). (c) The directional derivative of the function f at the point (7, 7) in the direction of the vector (3, 4). (d) The maximum rate of change of the function f at the point (7,0). (e) The direction in which the function f decreases fastest at the point (7,0).

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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Question 2. Let f(x, y) = 5xy² + sin(x + y). Find the following: (a) The gradient of f(x, y). (b) The gradient of the function f at the point (π, π). (c) The directional derivative of the function f at the point (π, π) in the direction of the vector (3, 4). (d) The maximum rate of change of the function f at the point (π, 0). (e) The direction in which the function f decreases fastest at the point (π, 0).
Transcribed Image Text:Question 2. Let f(x, y) = 5xy² + sin(x + y). Find the following: (a) The gradient of f(x, y). (b) The gradient of the function f at the point (π, π). (c) The directional derivative of the function f at the point (π, π) in the direction of the vector (3, 4). (d) The maximum rate of change of the function f at the point (π, 0). (e) The direction in which the function f decreases fastest at the point (π, 0).
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