Find the Gradient Vector Field of the Scalar Function $f$ (That Is, Find the Conservative Vector Field

question 83

Short Answer

Find the gradient vector field of the scalar function $f$ . (That is, find the conservative vector field $\mathbf { F }$ for the potential function $f$ of $\mathbf { F }$ .)
$$f ( x , y , z ) = 6 x y ^ { 3 } + 8 y z ^ { 4 }$$

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Definitions:

Diseconomies of Scale

Occur when a company or business grows so large that the costs per unit increase.

Management

The process of directing and controlling a group of people or an organization to achieve a set goal by using resources efficiently and effectively.

Information Dissemination

Information dissemination is the process of distributing or spreading information to a wide audience, often through various media or communication channels.

Returns to Scale

The rate at which output increases as inputs are proportionally increased, indicating either increasing, constant, or decreasing efficiency in production.