Determine Whether or Not Vector Field Is Conservative $f$ Such That $\mathbf { F } = \nabla f$

question 38

Short Answer

Determine whether or not vector field is conservative. If it is conservative, find a function $f$ such that $\mathbf { F } = \nabla f$ .
$$\mathbf { F } ( x , y , z ) = 18 x \mathbf { i } + 10 y \mathbf { j } + 4 z \mathbf { k }$$

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Definitions:

Proposition

A declaration that conveys an assessment or viewpoint.

Standard Form

A universally recognized method of displaying information or arguments for ease of understanding and analysis.

Implicit Propositions

Statements that are assumed within an argument but not explicitly stated.

Syllogisms

A method of logic where a conclusion is derived from two presented or assumed statements (premises), both containing a shared or middle term that is absent in the conclusion.