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Consider the surface S of equation z²-2x² + y²-x= 0 and let P (2, 3, 1) be a point at S. Suppose z is an implicit function of x and y in a neighborhood of point P. Consider the following statements: I. There is no direction for which the directional derivative of z in P is -40. II. The maximum directional derivative of z at point P is V13 II. The vector Vz (P) is unitary. Of the above statements are TRUE: To all. B) None. C) Only II. D) I and II.

Consider the surface S of equation z²-2x² + y²-x= 0 and let P (2, 3, 1) be a point at S. Suppose z is an implicit function of x and y in a neighborhood of point P. Consider the following statements: I. There is no direction for which the directional derivative of z in P is -40. II. The maximum directional derivative of z at point P is V13 II. The vector Vz (P) is unitary. Of the above statements are TRUE: To all. B) None. C) Only II. D) I and II.

Advanced Engineering Mathematics
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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8. Consider the surface S of equation z2-2x? + y²-x= 0 and let P (2, 3, 1) be a point at S. Suppose z is an implicit function of x and y in a neighborhood of point P. Consider the following statements: I. There is no direction for which the directional derivative of z in P is -40. II. The maximum directional derivative of z at point P is V13 III. The vector Vz (P) is unitary. 2 Of the above statements are TRUE: To all. B) None. C) Only II. D) I and II.
Transcribed Image Text:8. Consider the surface S of equation z2-2x? + y²-x= 0 and let P (2, 3, 1) be a point at S. Suppose z is an implicit function of x and y in a neighborhood of point P. Consider the following statements: I. There is no direction for which the directional derivative of z in P is -40. II. The maximum directional derivative of z at point P is V13 III. The vector Vz (P) is unitary. 2 Of the above statements are TRUE: To all. B) None. C) Only II. D) I and II.
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