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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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 18EQ
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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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