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The figure below shows various gradient vectors of a function f. Determine whether each of the following statements is TRUE or FALSE. In each case explain or justify your answer. (a) Vf(-2,2) = –4î + 33 (b) fz(2,–1) = -î and fy(2, –1) = }. (c) f(2.02,2) > f(2, 2) (d) The tangent line to the level (contour) curve at the point (2,1) has i – j as its direction vector.

The figure below shows various gradient vectors of a function f. Determine whether each of the following statements is TRUE or FALSE. In each case explain or justify your answer. (a) Vf(-2,2) = –4î + 33 (b) fz(2,–1) = -î and fy(2, –1) = }. (c) f(2.02,2) > f(2, 2) (d) The tangent line to the level (contour) curve at the point (2,1) has i – j as its direction vector.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 34E
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Gradient vector field and directional derivatives. Please answer (b) only and explain reasoning

11. The figure below shows various gradient vectors of a function f. Determine whether each of the following statements is TRUE or FALSE. In each case explain or justify your answer. -4 -2 (a) Vf(-2,2) = –48 + 3ĵ (b) fa(2, –1) = -i and fy(2, –1) = j. (c) f(2.02, 2) > f(2, 2) (d) The tangent line to the level (contour) curve at the point (2,1) has i – j as its direction vector.
Transcribed Image Text:11. The figure below shows various gradient vectors of a function f. Determine whether each of the following statements is TRUE or FALSE. In each case explain or justify your answer. -4 -2 (a) Vf(-2,2) = –48 + 3ĵ (b) fa(2, –1) = -i and fy(2, –1) = j. (c) f(2.02, 2) > f(2, 2) (d) The tangent line to the level (contour) curve at the point (2,1) has i – j as its direction vector.
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