CODE/CALC ET 3-HOLE
2nd Edition
ISBN: 9781323178522
Author: Briggs
Publisher: PEARSON
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Textbook Question
Chapter 12.6, Problem 34E
Interpreting directional derivatives A function f and a point P are given. Let θ correspond to the direction of the directional derivative.
- a. Find the gradient and evaluate it at P.
- b. Find the angles θ (with respect to the positive x-axis) associated with the directions of maximum increase, maximum decrease, and zero change.
- c. Write the directional derivative at P as a function of θ; call this function g.
- d. Find the value of θ that maximizes g(θ) and find the maximum value.
- e. Verify that the value of θ that maximizes g corresponds to the direction of the gradient. Verify that the maximum value of g equals the magnitude of the gradient.
33.
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