Estimate fx and fy at point C. 4. 2 0- fx(C) ≈ -20 fy(C) ~ -2.5 0 -2 Incorrect 70 50 30 10 (Use decimal notation. Give your answer to one decimal pla -30 -10- 30 -50 -70
Estimate fx and fy at point C. 4. 2 0- fx(C) ≈ -20 fy(C) ~ -2.5 0 -2 Incorrect 70 50 30 10 (Use decimal notation. Give your answer to one decimal pla -30 -10- 30 -50 -70
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Estimating Partial Derivatives at a Point
To estimate the partial derivatives \( f_x \) and \( f_y \) at point C, refer to the contour graph provided.
#### Graph Explanation
The graph provided is a contour map of a function \( f(x,y) \). Key features include:
- **Axes**: The \( x \)-axis ranges from -4 to 4, and the \( y \)-axis ranges from -4 to 4. Each unit is equally spaced.
- **Contour Lines**: Each contour line represents a constant value of \( f(x,y) \), with labels indicating specific function values. Lines are labeled \( 70 \), \( 50 \), \( 30 \), \( 10 \), \(-10 \), \(-20 \), \(-30 \), and so on.
- **Points of Interest**: Specific points marked on the graph include points A, B, and C.
The aim is to estimate:
- \( f_x(C) \) (partial derivative with respect to \( x \) at point C)
- \( f_y(C) \) (partial derivative with respect to \( y \) at point C)
(Use decimal notation. Give your answer to one decimal place.)
#### Estimate \( f_x(C) \)
\[ f_x(C) \approx -2.5 \]
#### Estimate \( f_y(C) \)
\[ f_y(C) \approx 0 \]
**Note**: The value \( f_y(C) \approx 0 \) is marked as incorrect in the provided answer box.
For these estimations, consider the slope and spacing of the contour lines near point C. Closer and steeper lines suggest a larger derivative, while more gradually spaced lines suggest a smaller derivative.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F816cc47c-f059-4914-940d-8196a7c7af6b%2F2a02fb0e-27e4-4db4-a2f6-45920dea14c2%2F3acf9jj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Estimating Partial Derivatives at a Point
To estimate the partial derivatives \( f_x \) and \( f_y \) at point C, refer to the contour graph provided.
#### Graph Explanation
The graph provided is a contour map of a function \( f(x,y) \). Key features include:
- **Axes**: The \( x \)-axis ranges from -4 to 4, and the \( y \)-axis ranges from -4 to 4. Each unit is equally spaced.
- **Contour Lines**: Each contour line represents a constant value of \( f(x,y) \), with labels indicating specific function values. Lines are labeled \( 70 \), \( 50 \), \( 30 \), \( 10 \), \(-10 \), \(-20 \), \(-30 \), and so on.
- **Points of Interest**: Specific points marked on the graph include points A, B, and C.
The aim is to estimate:
- \( f_x(C) \) (partial derivative with respect to \( x \) at point C)
- \( f_y(C) \) (partial derivative with respect to \( y \) at point C)
(Use decimal notation. Give your answer to one decimal place.)
#### Estimate \( f_x(C) \)
\[ f_x(C) \approx -2.5 \]
#### Estimate \( f_y(C) \)
\[ f_y(C) \approx 0 \]
**Note**: The value \( f_y(C) \approx 0 \) is marked as incorrect in the provided answer box.
For these estimations, consider the slope and spacing of the contour lines near point C. Closer and steeper lines suggest a larger derivative, while more gradually spaced lines suggest a smaller derivative.
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