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43. Find the gradient of the function f(x, y, z) = x²e»²².

43. Find the gradient of the function f(x, y, z) = x²e»²².

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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984 CHAPTER 14 Partial Derivatives dz 42. If cos(xyz) = 1 + x²y² + z², find and дz ду əx 43. Find the gradient of the function f(x, y, z) = x²e²². 44. (a) When is the directional derivative of f a maximum? (b) When is it a minimum? (c) When is it 0? (d) When is it half of its maximum value? 45-46 Find the directional derivative of f at the given point in the indicated direction. 45. f(x, y) = x²e, (-2, 0), adding in the direction toward the point (2, -3) sh 46. f(x, y, z) = x²y + x√1 + z, in the direction of v = 2i + j ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 5 2.2 60 70 65 55 2 47. Find the maximum rate of change of f(x, y) = x²y + √y at the point (2, 1). In which direction does it occur? 18 (1, 2, 3), 48. Find the direction in which f(x, y, z) = zey increases most rapidly at the point (0, 1, 2). What is the maximum rate of increase? 80 - 2k BUS. CARE 49. The contour map shows wind speed in knots during Hurri- cane Andrew on August 24, 1992. Use it to estimate the value of the directional derivative of the wind speed at Homestead, Florida, in the direction of the eye of the hurricane. 75 AL 70 65 60 Homestead 52. f(x, 53. f(x, 54. f(x, 55-56 the set i 55. f re 56. f FA 57. U E 58. 59 m 5
Transcribed Image Text:984 CHAPTER 14 Partial Derivatives dz 42. If cos(xyz) = 1 + x²y² + z², find and дz ду əx 43. Find the gradient of the function f(x, y, z) = x²e²². 44. (a) When is the directional derivative of f a maximum? (b) When is it a minimum? (c) When is it 0? (d) When is it half of its maximum value? 45-46 Find the directional derivative of f at the given point in the indicated direction. 45. f(x, y) = x²e, (-2, 0), adding in the direction toward the point (2, -3) sh 46. f(x, y, z) = x²y + x√1 + z, in the direction of v = 2i + j ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 5 2.2 60 70 65 55 2 47. Find the maximum rate of change of f(x, y) = x²y + √y at the point (2, 1). In which direction does it occur? 18 (1, 2, 3), 48. Find the direction in which f(x, y, z) = zey increases most rapidly at the point (0, 1, 2). What is the maximum rate of increase? 80 - 2k BUS. CARE 49. The contour map shows wind speed in knots during Hurri- cane Andrew on August 24, 1992. Use it to estimate the value of the directional derivative of the wind speed at Homestead, Florida, in the direction of the eye of the hurricane. 75 AL 70 65 60 Homestead 52. f(x, 53. f(x, 54. f(x, 55-56 the set i 55. f re 56. f FA 57. U E 58. 59 m 5
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