Consider the function f(z, y, z) = 5z - 3zy + ryz %3D a. At the point (3,4, 5), what is the directional derivative of f(2, y, z) in the direction i +j-k? Give your answer to one decimal place. Give a numerical answer only. Directional Derivative = b. What is the direction of the maximum rate of change of f at (3, 4, 5)? Give your answer in vector form such as (1, 1,1). Do not use spaces. Direction = C. What is the maximum rate of change? Give your answer to one decimal place. Give a numerical answer donly. Maximum rate of change

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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empt%3D453632&cmid%3659607&page=D1
Consider the function
f(z, y, z) = 5z – 3ry+ ryz
a. At the point (3, 4, 5), what is the directional derivative of
f(E,y.z) in the direction i+j- k? Give your answer to one
decimal place. Give a numerical answer only.
Directional Derivative =
b. What is the direction of the maximum rate of change of f at
(3, 4, 5)? Give your answer in vector form such as (1, 1,1). Do not
use spaces.
Direction =
C. What is the maximum rate of change? Give your answer to one
decimal place. Give a numerical answer only.
Maximum rate of change =
Transcribed Image Text:empt%3D453632&cmid%3659607&page=D1 Consider the function f(z, y, z) = 5z – 3ry+ ryz a. At the point (3, 4, 5), what is the directional derivative of f(E,y.z) in the direction i+j- k? Give your answer to one decimal place. Give a numerical answer only. Directional Derivative = b. What is the direction of the maximum rate of change of f at (3, 4, 5)? Give your answer in vector form such as (1, 1,1). Do not use spaces. Direction = C. What is the maximum rate of change? Give your answer to one decimal place. Give a numerical answer only. Maximum rate of change =
Expert Solution
Step 1

Given function is

f(x,y,z)=5x23xy+xyz

To find the directional derivative of the above function at the point (3,4,5) in the direction of the below vector.

v = i + j - k

steps

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