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If Vf = F, then F is called a potential vector field, and f is called a conservative function. True O False

If Vf = F, then F is called a potential vector field, and f is called a conservative function. True O False

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Question 11 If \(\nabla f = \vec{F}\), then \(\vec{F}\) is called a potential vector field, and \(f\) is called a conservative function. - ⦿ True - ⦿ False --- This question evaluates your understanding of potential vector fields and conservative functions in the context of vector calculus. Specifically, the question states that if the gradient of a function \(f\) (denoted by \(\nabla f\)) is equal to a vector field \(\vec{F}\), then this vector field \(\vec{F}\) is called a potential vector field, and the function \(f\) is referred to as a conservative function. **Terminologies:** - **Potential Vector Field**: A vector field \(\vec{F}\) that can be expressed as the gradient of some scalar function \(f\). - **Conservative Function**: A scalar function \(f\) whose gradient results in a vector field. Answer options provided are: - True - False
Transcribed Image Text:### Question 11 If \(\nabla f = \vec{F}\), then \(\vec{F}\) is called a potential vector field, and \(f\) is called a conservative function. - ⦿ True - ⦿ False --- This question evaluates your understanding of potential vector fields and conservative functions in the context of vector calculus. Specifically, the question states that if the gradient of a function \(f\) (denoted by \(\nabla f\)) is equal to a vector field \(\vec{F}\), then this vector field \(\vec{F}\) is called a potential vector field, and the function \(f\) is referred to as a conservative function. **Terminologies:** - **Potential Vector Field**: A vector field \(\vec{F}\) that can be expressed as the gradient of some scalar function \(f\). - **Conservative Function**: A scalar function \(f\) whose gradient results in a vector field. Answer options provided are: - True - False
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