Let $F _ { 1 } ( x , y ) = y ^ { 5 } - 10 x y + \cos y$

question 38

Essay

Let $F _ { 1 } ( x , y ) = y ^ { 5 } - 10 x y + \cos y$ Find a function $F_{2}(x, y)$ , such that $\vec{F}=F_{1} \vec{i}+F_{2} \vec{j}$ is a gradient field.

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Definitions:

Shutdown Point

The level of operations at which a business does not generate enough revenue to cover its variable costs, leading to a temporary or permanent cessation of production.

Average Variable Cost

The total variable costs of production divided by the quantity of output produced, representing the cost of producing one more unit of output.

Short Run

A period in economics where at least one input is fixed and cannot be changed, limiting the response of a firm to changes in demand or production.

Shutdown Point

The level of production and corresponding price at which a business's total revenue exactly equals its total variable costs, beyond which the business would start to incur losses.