Consider the following statements about the surface of equation 2 = ye- – 2xy? and the point P(0,-2) in its domain: I) If one calculates the directional derivative of z in the direction of any vector w E R?, one is certain that Dwz(P) < V37. II) There is no direction from P such that the directional derivative of z calculated in that direction gives 1. II) The value of the directional derivative of z at point P calculated in the direction of the vector u = (3, 4) is equal to -14. Of the above statements are TRUE: A) Only I. B) None. C) Only II. D) Only I and III.
Consider the following statements about the surface of equation 2 = ye- – 2xy? and the point P(0,-2) in its domain: I) If one calculates the directional derivative of z in the direction of any vector w E R?, one is certain that Dwz(P) < V37. II) There is no direction from P such that the directional derivative of z calculated in that direction gives 1. II) The value of the directional derivative of z at point P calculated in the direction of the vector u = (3, 4) is equal to -14. Of the above statements are TRUE: A) Only I. B) None. C) Only II. D) Only I and 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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Transcribed Image Text:Consider the following statements about the surface of equation
z = ye- – 2xy?
and the point P(0,-2) in its domain:
I)
If one calculates the directional derivative of z in the direction of
any vector w E R?, one is certain that Duz(P) < V37.
I)
There is no direction from P such that the directional derivative of z
calculated in that direction gives 1.
The value of the directional derivative of z at point P calculated in
I)
the direction of the vector u = (3, 4) is equal to -14.
Of the above statements are TRUE:
A) Only I.
B) None.
C) Only II.
D) Only I and III.
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