Consider the following statements about the surface of the equation z = 2x / (ln (y) +1) - (y + 1) / x and the point P (−2, 1) in its domain: I. The value of the least directional derivative of z at point P is −√106. II. The directional derivative of z at point P is maximum if it is calculated in the direction of the vector w = (2, 5). III. There is no direction from P such that the directional derivative of z computed in such address as a result of −6. Of the above statements are TRUE: A) Only the I. B) Only III. C) None. D) Only II.

Consider the following statements about the surface of the equation z = 2x / (ln (y) +1) - (y + 1) / x and the point P (−2, 1) in its domain: I. The value of the least directional derivative of z at point P is −√106. II. The directional derivative of z at point P is maximum if it is calculated in the direction of the vector w = (2, 5). III. There is no direction from P such that the directional derivative of z computed in such address as a result of −6. Of the above statements are TRUE: A) Only the I. B) Only III. C) None. D) Only II.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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Question

II. The directional derivative of z at point P is maximum if it is calculated in the direction of the vector w = (2, 5).
III. There is no direction from P such that the directional derivative of z computed in such
address as a result of −6.
Of the above statements are TRUE:

A) Only the I.
B) Only III.
C) None.
D) Only II.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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