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.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

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