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? Question Draw the gradient f( − 1, 1), starting at ( − 1, 1), on the contour map of f(x, y) = xy. The contour map should have x and y in [ – 2, 2]. What is the point where the tip of the gradient ends? - (Give the point in traditional notation.) Hint

? Question Draw the gradient f( − 1, 1), starting at ( − 1, 1), on the contour map of f(x, y) = xy. The contour map should have x and y in [ – 2, 2]. What is the point where the tip of the gradient ends? - (Give the point in traditional notation.) Hint

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 Draw the gradient \( \vec{\nabla} f(-1,1) \), starting at \((-1,1)\), on the contour map of \( f(x,y) = xy \). The contour map should have \( x \) and \( y \) in \([-2, 2]\). What is the point where the tip of the gradient ends? (Note: Give the point in traditional notation.) ### Hint To determine where the tip of the gradient ends, follow these steps: 1. **Calculate the Gradient**: Calculate the gradient vector \( \vec{\nabla} f(x,y) \) of the function \( f(x, y) = xy \). 2. **Evaluate at Given Point**: Evaluate the gradient vector at the point \((-1,1)\). 3. **Graphical Representation**: Draw this evaluated gradient vector on the contour map of \( f(x,y) \). 4. **Determine the End Point**: Identify the coordinates of the tip of the gradient vector. The contour map of \( f(x,y) = xy \) should depict a grid with \( x \) and \( y \) ranging from \([-2, 2]\). Ensure to mark the evaluated points clearly and show the direction of the gradient vector.
Transcribed Image Text:### Question Draw the gradient \( \vec{\nabla} f(-1,1) \), starting at \((-1,1)\), on the contour map of \( f(x,y) = xy \). The contour map should have \( x \) and \( y \) in \([-2, 2]\). What is the point where the tip of the gradient ends? (Note: Give the point in traditional notation.) ### Hint To determine where the tip of the gradient ends, follow these steps: 1. **Calculate the Gradient**: Calculate the gradient vector \( \vec{\nabla} f(x,y) \) of the function \( f(x, y) = xy \). 2. **Evaluate at Given Point**: Evaluate the gradient vector at the point \((-1,1)\). 3. **Graphical Representation**: Draw this evaluated gradient vector on the contour map of \( f(x,y) \). 4. **Determine the End Point**: Identify the coordinates of the tip of the gradient vector. The contour map of \( f(x,y) = xy \) should depict a grid with \( x \) and \( y \) ranging from \([-2, 2]\). Ensure to mark the evaluated points clearly and show the direction of the gradient vector.
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