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Which point has the gradient vector with the smallest magnitude? A

Which point has the gradient vector with the smallest magnitude? A

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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## Gradient Vector Magnitude Analysis ### Question Which point has the gradient vector with the smallest magnitude? ### Image Description The image consists of a contour plot with labeled points A, B, and C. The contours represent some scalar field, with lines closer together indicating regions of higher gradient (steeper slopes), and lines further apart representing regions of lower gradient (gentler slopes). #### Contour Plot Details - **Point A** is positioned on the left side of the plot within a region where the contour lines are densely packed. - **Point B** is located toward the center-right of the plot where the contour lines are moderately spaced. - **Point C** is on the right side of the plot, situated within a region where the contour lines are spaced far apart. ### Analysis - **Point A**: The density of the contour lines at this point implies a high gradient magnitude. - **Point B**: The contour lines are closer than at point C but not as dense as at point A, indicating a moderate gradient magnitude. - **Point C**: The widely spaced contour lines suggest the smallest gradient magnitude. ### Conclusion The point with the gradient vector of the smallest magnitude is most likely to be **Point C**. ### Answer Options - ⭕ B -
Transcribed Image Text:## Gradient Vector Magnitude Analysis ### Question Which point has the gradient vector with the smallest magnitude? ### Image Description The image consists of a contour plot with labeled points A, B, and C. The contours represent some scalar field, with lines closer together indicating regions of higher gradient (steeper slopes), and lines further apart representing regions of lower gradient (gentler slopes). #### Contour Plot Details - **Point A** is positioned on the left side of the plot within a region where the contour lines are densely packed. - **Point B** is located toward the center-right of the plot where the contour lines are moderately spaced. - **Point C** is on the right side of the plot, situated within a region where the contour lines are spaced far apart. ### Analysis - **Point A**: The density of the contour lines at this point implies a high gradient magnitude. - **Point B**: The contour lines are closer than at point C but not as dense as at point A, indicating a moderate gradient magnitude. - **Point C**: The widely spaced contour lines suggest the smallest gradient magnitude. ### Conclusion The point with the gradient vector of the smallest magnitude is most likely to be **Point C**. ### Answer Options - ⭕ B -
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