Let $\vec{F}=\left(4 x^{3}-y^{6} \sin x\right) \vec{i}+\left(6 y^{5} \cos x+4 z\right) \vec{j}+4 y \vec{k}$

question 20

Essay

Let $\vec{F}=\left(4 x^{3}-y^{6} \sin x\right) \vec{i}+\left(6 y^{5} \cos x+4 z\right) \vec{j}+4 y \vec{k}$ Show that $\vec{F}$ is a gradient field by finding its potential function.

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Definitions:

Sherman Antitrust Act

The Sherman Antitrust Act is a landmark U.S. law passed in 1890 aimed at preventing anticompetitive practices and promoting fair competition.

Antitrust Policy

Legislation enacted by federal or state government to prevent new monopolies from forming and to break up those that already exist in order to promote competition and ensure fair practices in the marketplace.

Monopolies

A market structure characterized by a single seller who has exclusive control over a product or service, with no close substitutes.

Product Differentiation

The practice of highlighting the unique features of a product or service to increase its appeal to a targeted market segment.