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The contour diagram of the function f(x,y) is given below

The contour diagram of the function f(x,y) is given below

Advanced Engineering Mathematics
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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The contour diagram of the function f(x,y) is given below 3 ·0 # 1.5 10 20 60 10 25 2 1 0.5 -30 % 50 05 O 1.5 concave down 50 unable to determine concave up 70- V 110 130 25 fyy fxx ES What verbal description applies to the slopes in the y direction as y increases? 107 The y slopes are negative and getting steeper. 1107 130 The y slopes are negative and getting less steep. 150 1707 The y slopes are positive and getting less steep. 2-190 The y slopes are positive and getting steeper. Consider the surface near (2.1) in the y direction. What concavity in the y direction? Hint: sketch the intersection of the surface with x=2. Determine the sign of the second derivatives fax and fyy. 1. Positive 2. Negative 3. Zero
Transcribed Image Text:The contour diagram of the function f(x,y) is given below 3 ·0 # 1.5 10 20 60 10 25 2 1 0.5 -30 % 50 05 O 1.5 concave down 50 unable to determine concave up 70- V 110 130 25 fyy fxx ES What verbal description applies to the slopes in the y direction as y increases? 107 The y slopes are negative and getting steeper. 1107 130 The y slopes are negative and getting less steep. 150 1707 The y slopes are positive and getting less steep. 2-190 The y slopes are positive and getting steeper. Consider the surface near (2.1) in the y direction. What concavity in the y direction? Hint: sketch the intersection of the surface with x=2. Determine the sign of the second derivatives fax and fyy. 1. Positive 2. Negative 3. Zero
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