(1) Values of z = f(x, y) and its derivatives are given in the table below und reans contour diagram is to the right (contours are labelled, but for reference, the dashed contours are even and dark contours are odd). Use them to answer the following questions. Make sure to justify all your work. 1.5 1.0 (x, y) f fx fy fax fyy fry (0,0) 0 und und und und und 0.5 -3 (1,0) =4 0 1 -1 2 (1, 1) 5.5 2 =1 1 1 ત્યાર (1,-1) 5.5 1 2 1 0.0 મુ ક ા માની શ (0, 1) -6 0 -1 #1 1 2 (-1,1) -5.5 -1 -2 1 2 1 (-1,0) 0 0 1 1 2 -0.5 (0, -1) -6 0 1 1 2 1 (-1,-1) -5.5 1 2 =1 #1 2 -1.0 (a) Identify which of the points in the table are critical points. -1.5 -1.0 -0.5 10.0 0.5 1.0 1.5 (b) Classify the critical points appearing in the table as minima, maxima or neither. Provide reasoning for each. (c) Find an equation for the tangent plane to f(x, y) at the point (1,-1). Write your answer in the form ax+by+cz = d. subiect to the constraint
(1) Values of z = f(x, y) and its derivatives are given in the table below und reans contour diagram is to the right (contours are labelled, but for reference, the dashed contours are even and dark contours are odd). Use them to answer the following questions. Make sure to justify all your work. 1.5 1.0 (x, y) f fx fy fax fyy fry (0,0) 0 und und und und und 0.5 -3 (1,0) =4 0 1 -1 2 (1, 1) 5.5 2 =1 1 1 ત્યાર (1,-1) 5.5 1 2 1 0.0 મુ ક ા માની શ (0, 1) -6 0 -1 #1 1 2 (-1,1) -5.5 -1 -2 1 2 1 (-1,0) 0 0 1 1 2 -0.5 (0, -1) -6 0 1 1 2 1 (-1,-1) -5.5 1 2 =1 #1 2 -1.0 (a) Identify which of the points in the table are critical points. -1.5 -1.0 -0.5 10.0 0.5 1.0 1.5 (b) Classify the critical points appearing in the table as minima, maxima or neither. Provide reasoning for each. (c) Find an equation for the tangent plane to f(x, y) at the point (1,-1). Write your answer in the form ax+by+cz = d. subiect to the constraint
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) Values of z = f(x, y) and its derivatives are given in the table below
und
reans
contour diagram is to the right (contours are labelled, but for reference, the dashed contours are even and
dark contours are odd). Use them to answer the following questions. Make sure to justify all your work.
1.5
1.0
(x, y)
f
fx
fy
fax fyy fry
(0,0)
0
und und
und
und
und
0.5
-3
(1,0)
=4
0
1 -1
2
(1, 1)
5.5
2
=1
1
1
ત્યાર
(1,-1)
5.5
1
2
1
0.0
મુ ક ા માની શ
(0, 1)
-6
0
-1
#1
1
2
(-1,1)
-5.5
-1
-2
1
2
1
(-1,0)
0
0
1
1
2
-0.5
(0, -1)
-6
0
1
1
2
1
(-1,-1)
-5.5
1
2
=1
#1
2
-1.0
(a) Identify which of the points in the table are critical points.
-1.5
-1.0
-0.5
10.0
0.5
1.0
1.5
(b) Classify the critical points appearing in the table as minima, maxima or neither. Provide reasoning for
each.
(c) Find an equation for the tangent plane to f(x, y) at the point (1,-1). Write your answer in the form
ax+by+cz = d.
subiect to the constraint
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