Multiple choice homework question For a differentiable function \( f \), a theorem states that the direction of maximum decrease is in the opposite direction as the gradient vector. In the proof of this theorem, which of the following properties is not used?(A) The magnitude of a unit vector is 1.(B) The Chain Rule for multivariable functions.(C) \( \cos \theta \) is a bounded function; in particular, it is greater than or equal to \(-1\).(D) The property that \(\mathbf{a} \cdot \mathbf{b} = \|\mathbf{a}\| \|\mathbf{b}\| \cos \theta\) where \(\theta\) is the angle between \(\mathbf{a}\) and \(\mathbf{b}\).(E) If the angle between two vectors is \(\pi\), then the two vectors have opposite direction.(F) All of the above properties were used in the proof.

Answered: Image /qna-images/answer/4575dc62-295f-4d8e-be5e-60a1f74aecf3.jpg

For a differentiable function f, a theorem states that the direction of maximum decrease is in the opposite direction as the gradient vector. In the proof this theorem, which of the following properties is not used? (A) The magnitude of a unit vector is 1. (B) The Chain Rule for multivariable functions. (C) cos is a bounded function; in particular, it is greater than or equal to -1. (D) The property that ā·b =||ā|||||cos✪ where ¤ is the angle between ã and b. (E) If the angle between two vectors is, then the two vectors have opposite direction.

For a differentiable function f, a theorem states that the direction of maximum decrease is in the opposite direction as the gradient vector. In the proof this theorem, which of the following properties is not used? (A) The magnitude of a unit vector is 1. (B) The Chain Rule for multivariable functions. (C) cos is a bounded function; in particular, it is greater than or equal to -1. (D) The property that ā·b =||ā|||||cos✪ where ¤ is the angle between ã and b. (E) If the angle between two vectors is, then the two vectors have opposite direction.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Help solve please!
Subject - account Please help me. Thankyou.
Least common multiple of 4 and 20
How to find the values and find it in excel
show work and why it might be negative if you get negative number please thank you
How many outcomes are possible on a 3 question, multiple choice quiz (with 3 choices each per question)?