Determine whether the statement " If f(x, y) = x + y, then −1 ≤ Du f(x, y) ≤ 1" is true or false. If it is false, explain why or give an example that shows it is false.
Determine whether the statement " If f(x, y) = x + y, then −1 ≤ Du f(x, y) ≤ 1" is true or false. If it is false, explain why or give an example that shows it is false.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
Related questions
Question
Determine whether the statement " If f(x, y) = x + y, then −1 ≤ Du f(x, y) ≤ 1" is true or false. If it is false, explain why or give an example that shows it is false.
Expert Solution
Step 1
If the statement "If , then for any unit vector u" is true or false.
Step 2
Examine the stated function:
Thus, first find the gradient of the stated function as:
Thus, the direction of maximum increase is stated by the unit vector:
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning