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If f(x, y) is differentiable near (x,y) = (a, b), and u is any unit vector, consider the following statements. (i) If Duf (a, b) > 0 and v = -u then Dyf(a, b) <0 (ii) Duf (a, b) may be greater than || Vf (a, b)|| (iii) If u is Duf(a, b) = 0 parallel to f (a, b) then

If f(x, y) is differentiable near (x,y) = (a, b), and u is any unit vector, consider the following statements. (i) If Duf (a, b) > 0 and v = -u then Dyf(a, b) <0 (ii) Duf (a, b) may be greater than || Vf (a, b)|| (iii) If u is Duf(a, b) = 0 parallel to f (a, b) then

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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Problem #1: If f(x, y) is differentiable near (x,y) = (a, b), and u is any unit vector, consider the consider the following statements. (i) If Duf(a, b) > 0 and v Dyf(a, b) <0 = -u then (ii) Duf (a, b) may be greater than || Vf (a, b)||| (iii) If u is parallel to f (a, b) then Duf (a,b) = 0 Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True, False, False, then you would enter '1,2,2' into the answer box below (without the quotes).
Transcribed Image Text:Problem #1: If f(x, y) is differentiable near (x,y) = (a, b), and u is any unit vector, consider the consider the following statements. (i) If Duf(a, b) > 0 and v Dyf(a, b) <0 = -u then (ii) Duf (a, b) may be greater than || Vf (a, b)||| (iii) If u is parallel to f (a, b) then Duf (a,b) = 0 Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True, False, False, then you would enter '1,2,2' into the answer box below (without the quotes).
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