The figure below shows the level curves of a function f(x, y) around a maximum or minimum, M. The 2- and y-axes are along the bottom and left edge of the figure, respectively. One of the points P and Q has coordinates (21,31) and the other has coordinates (2, 32). Suppose b>0 and ec> 0. Consider the two linear approximations to f given by f(x,y)≈a+b(x − x₁) + c(y - y₁), and (a) What is the relationship between the values of a and k? (Give your answer as an equation.) (b) What are the coordinates of P? P (c) Is M a maximum or a minimum?? (d) What can you say about the sign of the constants m and n? m?0, and 0. n f(x, y) k+m(x - 2) + n(y-32).
The figure below shows the level curves of a function f(x, y) around a maximum or minimum, M. The 2- and y-axes are along the bottom and left edge of the figure, respectively. One of the points P and Q has coordinates (21,31) and the other has coordinates (2, 32). Suppose b>0 and ec> 0. Consider the two linear approximations to f given by f(x,y)≈a+b(x − x₁) + c(y - y₁), and (a) What is the relationship between the values of a and k? (Give your answer as an equation.) (b) What are the coordinates of P? P (c) Is M a maximum or a minimum?? (d) What can you say about the sign of the constants m and n? m?0, and 0. n f(x, y) k+m(x - 2) + n(y-32).
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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Transcribed Image Text:The figure below shows the level curves of a function f(x, y) around a maximum or minimum, M. The x- and y-axes are along the bottom and left edge of the figure, respectively.
One of the points P and Q has coordinates (1,9₁) and the other has coordinates (x2, y2). Suppose b>0 and e > 0. Consider the two linear approximations to f given by
f(x, y) a+b(x − x₁) + c(y - y₁),
and
(a) What is the relationship between the values of a and k?
(Give your answer as an equation.)
(b) What are the coordinates of P?
(c) Is M a maximum or a minimum??
(d) What can you say about the sign of the constants m and n?
m
✓0, and
✓0.
n?
f(x, y) ≈k+m(x − x2) + n(y — y2).
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