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A function f and a point P are given. Let 9 correspond to the direction of the directional derivative. Complete parts a. through e. 1. P(1/1₁ -√²) f(x,y)=In (1 +6x² +5y²), P a. Find the gradient and evaluate it at P. 4√2 The gradient at P is 12 b. Find the angles (with respect to the positive x-axis) between 0 and 2x associated with the directions of maximum increase, maximum decrease, and zero change. What angles are associated with the direction of maximum increase? (Type your answer in radians. Type an exact answer terms of Use a comma to separate answers as needed.)

A function f and a point P are given. Let 9 correspond to the direction of the directional derivative. Complete parts a. through e. 1. P(1/1₁ -√²) f(x,y)=In (1 +6x² +5y²), P a. Find the gradient and evaluate it at P. 4√2 The gradient at P is 12 b. Find the angles (with respect to the positive x-axis) between 0 and 2x associated with the directions of maximum increase, maximum decrease, and zero change. What angles are associated with the direction of maximum increase? (Type your answer in radians. Type an exact answer terms of Use a comma to separate answers as needed.)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.2: Power Functions
Problem 17E: Tsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height...
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A function f and a point P are given. Let 9 correspond to the direction of the directional derivative. Complete parts a. through e. f(x,y) = In (1 +6x² +5y²), P ( 2₁ -√²) a. Find the gradient and evaluate it at P. 4√2 5 The gradient at P is 12 25 (...) b. Find the angles 9 (with respect to the positive x-axis) between 0 and 2 associated with the directions of maximum increase, maximum decrease, and zero change. What angles are associated with the direction of maximum increase? (Type your answer in radians. Type an exact answer in terms of . Use a comma to separate answers as needed.)
Transcribed Image Text:A function f and a point P are given. Let 9 correspond to the direction of the directional derivative. Complete parts a. through e. f(x,y) = In (1 +6x² +5y²), P ( 2₁ -√²) a. Find the gradient and evaluate it at P. 4√2 5 The gradient at P is 12 25 (...) b. Find the angles 9 (with respect to the positive x-axis) between 0 and 2 associated with the directions of maximum increase, maximum decrease, and zero change. What angles are associated with the direction of maximum increase? (Type your answer in radians. Type an exact answer in terms of . Use a comma to separate answers as needed.)
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