1. The contour diagram for a function f(x, y) is shown below. Use it to answer the following questions: 0.5 00 -0.5 -1.0 -15 16 12 08 0.4 0.6 -1.0 24 1.93 22 0.6 2.15 -04- 1.93 2.092 (2.42 24 1.4 12 0.8 0.4 (a) Identify the seven critical points of the function by giving their approximate coordi- nates, and say whether each one is a local max, local min, or saddle. For each one, describe in words how you know. (b) The point P is located at (0.7.-1). Approximate fr(P) and f,(P). (c) Give the (approximate) coordinates of a point Q such that is not a critical point of f, but fy(Q) = 0. Explain in words why your answer works (note that there are lots of possibilities here. You just have to find one).
1. The contour diagram for a function f(x, y) is shown below. Use it to answer the following questions: 0.5 00 -0.5 -1.0 -15 16 12 08 0.4 0.6 -1.0 24 1.93 22 0.6 2.15 -04- 1.93 2.092 (2.42 24 1.4 12 0.8 0.4 (a) Identify the seven critical points of the function by giving their approximate coordi- nates, and say whether each one is a local max, local min, or saddle. For each one, describe in words how you know. (b) The point P is located at (0.7.-1). Approximate fr(P) and f,(P). (c) Give the (approximate) coordinates of a point Q such that is not a critical point of f, but fy(Q) = 0. Explain in words why your answer works (note that there are lots of possibilities here. You just have to find one).
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:1. The contour diagram for a function f(x, y) is shown below. Use it to answer the following
questions:
0.5
0.0
-0.5
-1.0
-1.5
1.6
1.2
0.8
0.4
-1.0
0.6
24
1.2
2.15
(242)
1.93
22
-0.5
0.6
2.15-
-04-
1.8-
1.93
-1.6-
0.0
2.092
0.5
(2.42
-2.2-
24
0.6
1.0
1.8
1.2
0.8
0.4
(a) Identify the seven critical points of the function by giving their approximate coordi-
nates, and say whether each one is a local max, local min, or saddle. For each one,
describe in words how you know.
(b) The point P is located at (0.7,-1). Approximate fr(P) and f, (P).
(c) Give the (approximate) coordinates of a point Q such that is not a critical point
of f, but fy(Q) = 0. Explain in words why your answer works (note that there are
lots of possibilities here. You just have to find one).
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