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36. The derivative of f(x, y, z) at a point P is greatest in the direction of v=i+jk. In this direction, the value of the derivative is 2√3. a. What is Vf at P? Give reasons for your answer. b. What is the derivative of f at P in the direction of i + j?

36. The derivative of f(x, y, z) at a point P is greatest in the direction of v=i+jk. In this direction, the value of the derivative is 2√3. a. What is Vf at P? Give reasons for your answer. b. What is the derivative of f at P in the direction of i + j?

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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14.6 Tangent Planes and Differentials 839 36. The derivative of f(x, y, z) at a point P is greatest in the direction of v = i +j - k. In this direction, the value of the derivative is 2V3. the a. What is Vf at P? Give reasons for your answer. b. What is the derivative off at P in the direction of i +j? 37. Directional derivatives and scalar components How is the derivative of a differentiable function f(x, y, z) at a point Po in the direction of a unit vector u related to the scalar component of (Vf)P, in the direction of u? Give reasons for your answer. es of 38. Directional derivatives and partial derivatives Assuming that the necessary derivatives of f(x, y, z) are defined, how are Df, Dif, and Df related to f, fy, and f.? Give reasons for your answer. 39. Lines in the xy-plane Show that A(x xo) + B(y-yo) is an equation for the line in the xy-plane through the point (xo. Yo) normal to the vector N 40 Thelolgn = Ai + Bj. the
Transcribed Image Text:14.6 Tangent Planes and Differentials 839 36. The derivative of f(x, y, z) at a point P is greatest in the direction of v = i +j - k. In this direction, the value of the derivative is 2V3. the a. What is Vf at P? Give reasons for your answer. b. What is the derivative off at P in the direction of i +j? 37. Directional derivatives and scalar components How is the derivative of a differentiable function f(x, y, z) at a point Po in the direction of a unit vector u related to the scalar component of (Vf)P, in the direction of u? Give reasons for your answer. es of 38. Directional derivatives and partial derivatives Assuming that the necessary derivatives of f(x, y, z) are defined, how are Df, Dif, and Df related to f, fy, and f.? Give reasons for your answer. 39. Lines in the xy-plane Show that A(x xo) + B(y-yo) is an equation for the line in the xy-plane through the point (xo. Yo) normal to the vector N 40 Thelolgn = Ai + Bj. the
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