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Using the contour map, answer the questions that follow. (a) Estimate fr and fy at point B. (b) Estimate fa and fy at point C. (c) What is the sign of fa at point B? (d) What is the sign of f, at point B? 2 2 -20 B 8. -10 70 50 30 /// -30 .C 10 0. -10 10 -4 02 Rogawski et al., Calculus: Early Transcendentals, 4e, © 2019 W. H. Freeman and Company -30 111 -50 -70

Using the contour map, answer the questions that follow. (a) Estimate fr and fy at point B. (b) Estimate fa and fy at point C. (c) What is the sign of fa at point B? (d) What is the sign of f, at point B? 2 2 -20 B 8. -10 70 50 30 /// -30 .C 10 0. -10 10 -4 02 Rogawski et al., Calculus: Early Transcendentals, 4e, © 2019 W. H. Freeman and Company -30 111 -50 -70

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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### Using the contour map, answer the questions that follow. #### Contour Map Description The contour map presents a gradient field with contour lines representing different function values. The axes are marked with \(x\) and \(y\), and several contour lines are labeled with their respective values ranging from -70 to 70. Specific points \( A \), \( B \), and \( C \) are indicated, presumably where questions will be analyzed. **Figure:** ``` Contour Map with Points A, B, C ``` - **Axes:** \( x \)-axis and \( y \)-axis - **Contour lines and their values:** - Negative values as low as -70 - Positive values as high as 70 - **Notable Points:** - \( B \) at approximately (-2, 3) - \( C \) at approximately (2, 2) - \( A \) at approximately (3, -2) Source: Rogawski et al., *Calculus: Early Transcendentals, 4e*, © 2019 W. H. Freeman and Company #### Questions: (a) Estimate \( f_x \) and \( f_y \) at point \( B \). (b) Estimate \( f_x \) and \( f_y \) at point \( C \). (c) What is the sign of \( f_x \) at point \( B \)? (d) What is the sign of \( f_y \) at point \( B \)? #### Analysis: To estimate \( f_x \) and \( f_y \) at any point, observe the rate of change of the function in the horizontal (\( x \)-direction) and vertical (\( y \)-direction) by examining the contour lines close to the point in question. - \( f_x \): Rate of change of the function in the \( x \)-direction. - \( f_y \): Rate of change of the function in the \( y \)-direction. **Guidance:** - Closely spaced contour lines indicate a steep gradient (large value of \( f_x \) or \( f_y \)). - Widely spaced contour lines indicate a gentle gradient (small value of \( f_x \) or \( f_y \)). - For the sign determination: - If moving in the positive \( x \) (or \( y \))-direction leads to higher function values, \(
Transcribed Image Text:### Using the contour map, answer the questions that follow. #### Contour Map Description The contour map presents a gradient field with contour lines representing different function values. The axes are marked with \(x\) and \(y\), and several contour lines are labeled with their respective values ranging from -70 to 70. Specific points \( A \), \( B \), and \( C \) are indicated, presumably where questions will be analyzed. **Figure:** ``` Contour Map with Points A, B, C ``` - **Axes:** \( x \)-axis and \( y \)-axis - **Contour lines and their values:** - Negative values as low as -70 - Positive values as high as 70 - **Notable Points:** - \( B \) at approximately (-2, 3) - \( C \) at approximately (2, 2) - \( A \) at approximately (3, -2) Source: Rogawski et al., *Calculus: Early Transcendentals, 4e*, © 2019 W. H. Freeman and Company #### Questions: (a) Estimate \( f_x \) and \( f_y \) at point \( B \). (b) Estimate \( f_x \) and \( f_y \) at point \( C \). (c) What is the sign of \( f_x \) at point \( B \)? (d) What is the sign of \( f_y \) at point \( B \)? #### Analysis: To estimate \( f_x \) and \( f_y \) at any point, observe the rate of change of the function in the horizontal (\( x \)-direction) and vertical (\( y \)-direction) by examining the contour lines close to the point in question. - \( f_x \): Rate of change of the function in the \( x \)-direction. - \( f_y \): Rate of change of the function in the \( y \)-direction. **Guidance:** - Closely spaced contour lines indicate a steep gradient (large value of \( f_x \) or \( f_y \)). - Widely spaced contour lines indicate a gentle gradient (small value of \( f_x \) or \( f_y \)). - For the sign determination: - If moving in the positive \( x \) (or \( y \))-direction leads to higher function values, \(
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