The figure shows the level curves of a function f(x, y) around a maximum or a minimum M. One of the points P or Q has coordinates (#1, y₁) and the other has coordinates (#2, 32). Suppose b > 0 and c> 0. Consider the two linear approximations to f given by (a) What is the relationship between the values of a and k? A. a = -k B. a > k C.a

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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E35

The figure shows the level curves of a function f(x, y) around a maximum or a minimum M. One of the points P or Qhas coordinates (2₁, y₁) and the other has coordinates (x2, y2).
Suppose b > 0 and c > 0. Consider the two linear approximations to f given by
(a) What is the relationship between the values of a and k?
A. a = -k
B. a > k
C.a <k
D. a = k
(b) What are the coordinates of point P?
A. (12, Y2)
= B. (2₁, y₁)
(c) Is M a maximum or a minimum??
(d) Is the sign of m positive or negative??
(e) Is the sign of n positive or negative??
f(x,y) ~ a+b(x − x₁) + c(y - y₁),
f(x, y) ≈k+m(x − x2) + n(y — Y2).
2.4 F
Р
Q
Transcribed Image Text:The figure shows the level curves of a function f(x, y) around a maximum or a minimum M. One of the points P or Qhas coordinates (2₁, y₁) and the other has coordinates (x2, y2). Suppose b > 0 and c > 0. Consider the two linear approximations to f given by (a) What is the relationship between the values of a and k? A. a = -k B. a > k C.a <k D. a = k (b) What are the coordinates of point P? A. (12, Y2) = B. (2₁, y₁) (c) Is M a maximum or a minimum?? (d) Is the sign of m positive or negative?? (e) Is the sign of n positive or negative?? f(x,y) ~ a+b(x − x₁) + c(y - y₁), f(x, y) ≈k+m(x − x2) + n(y — Y2). 2.4 F Р Q
y
2.4
1.6
0.8
0
-0.8
-1.6
-2.4
-4.5
PO
P
-1.5
M
0
X
1.5
Q
0%
tm.
3
4.5
Transcribed Image Text:y 2.4 1.6 0.8 0 -0.8 -1.6 -2.4 -4.5 PO P -1.5 M 0 X 1.5 Q 0% tm. 3 4.5
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