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1. The figure shows the graph of some function of two variables, f. Without doing any calculations, decide whether the following are positive, negative, or zero. (There's no need to show work here.)

1. The figure shows the graph of some function of two variables, f. Without doing any calculations, decide whether the following are positive, negative, or zero. (There's no need to show work here.)

Advanced Engineering Mathematics
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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The figure shows the graph of a function of two variables, \( f \). Without performing any calculations, determine if the following are positive, negative, or zero. (No need to show work): a) \( f_x(a, b) \) b) \( f_y(a, b) \) c) \( f_x(c, d) \) d) \( f_y(c, d) \) e) \( f_x(0, 0) \) f) \( f_y(0, 0) \) **Diagram Explanation:** - The graph represents a surface, \( z = f(x, y) \), of a function of two variables. - Axes are labeled with \( x \), \( y \), and \( z \). - Points \((a, b, f(a, b))\) and \((c, d, f(c, d))\) are marked on the surface. - The arrows indicate the directions of the \( x \) and \( y \) axes with red and green arrows respectively, while the \( z \) axis is shown with a blue arrow. - Partial derivatives \( f_x \) and \( f_y \) represent the slopes along the \( x \)-axis and \( y \)-axis at specific points on the surface.
Transcribed Image Text:The figure shows the graph of a function of two variables, \( f \). Without performing any calculations, determine if the following are positive, negative, or zero. (No need to show work): a) \( f_x(a, b) \) b) \( f_y(a, b) \) c) \( f_x(c, d) \) d) \( f_y(c, d) \) e) \( f_x(0, 0) \) f) \( f_y(0, 0) \) **Diagram Explanation:** - The graph represents a surface, \( z = f(x, y) \), of a function of two variables. - Axes are labeled with \( x \), \( y \), and \( z \). - Points \((a, b, f(a, b))\) and \((c, d, f(c, d))\) are marked on the surface. - The arrows indicate the directions of the \( x \) and \( y \) axes with red and green arrows respectively, while the \( z \) axis is shown with a blue arrow. - Partial derivatives \( f_x \) and \( f_y \) represent the slopes along the \( x \)-axis and \( y \)-axis at specific points on the surface.
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