Let z = f (x, y) be a differentiable function on which it is known that the maximum directional derivative of z at a point P gives 5. Consider the following statements: I. The gradient vector of z in P is necessarily (4, 3) or (−4, −3). II. There is no vector u ∈ R2 such that Duz (P) = −7. III. If it is known that ∂z/∂x (P) = 3, then necessarily ∂z/∂y (P) = 4 or ∂z/∂y (P) = −4. Of the above statements are TRUE: A) II and III B) I and II C) Just II D) Just III
Let z = f (x, y) be a differentiable function on which it is known that the maximum directional derivative of z at a point P gives 5. Consider the following statements: I. The gradient vector of z in P is necessarily (4, 3) or (−4, −3). II. There is no vector u ∈ R2 such that Duz (P) = −7. III. If it is known that ∂z/∂x (P) = 3, then necessarily ∂z/∂y (P) = 4 or ∂z/∂y (P) = −4. Of the above statements are TRUE: A) II and III B) I and II C) Just II D) Just III
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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Let z = f (x, y) be a differentiable function on which it is known that the maximum directional derivative of z at a point P gives 5. Consider the following statements:
I. The gradient
II. There is no vector u ∈ R2 such that Duz (P) = −7.
III. If it is known that ∂z/∂x (P) = 3, then necessarily ∂z/∂y (P) = 4 or ∂z/∂y (P) = −4.
Of the above statements are TRUE:
A) II and III
B) I and II
C) Just II
D) Just III
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