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 (x1, y₁) and the other has coordinates (x2, y2). Suppose b < 0 and c> 0. Consider the two linear approximations to f given by 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? (x1,y1) Ⓒ (c) Is M a maximum or a minimum? minimum Ⓒ f(x, y) a+b(x-x₁) + c(y - y₁), f(x,y) k+m(x - x2) + n(y- y2).
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 (x1, y₁) and the other has coordinates (x2, y2). Suppose b < 0 and c> 0. Consider the two linear approximations to f given by 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? (x1,y1) Ⓒ (c) Is M a maximum or a minimum? minimum Ⓒ f(x, y) a+b(x-x₁) + c(y - y₁), f(x,y) k+m(x - x2) + n(y- y2).
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 (x₁, y₁) and the other has coordinates (x2, y2). Suppose 6 < 0 and c > 0. Consider the two linear approximations to f
given by
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?
(x1,y1) Ⓒ
(c) Is M a maximum or a minimum? minimum
(d) What can you say about the sign of the constants m and n?
m
0, and
n
Ⓒ 0.
f(x, y) ≈a+b(x − x₁) + c(y − yı),
f(x,y) ≈ k+m(x − x2) + n(y − y2).
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