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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
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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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.
Transcribed Image Text: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.
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