Determine Whether $\mathbf { F }$ Is Conservative $f$ Such That $\mathbf { F } = \nabla f . .$

question 12

Short Answer

Determine whether $\mathbf { F }$ is conservative. If so, find a function $f$ such that $\mathbf { F } = \nabla f . .$
$$\mathbf { F } ( x , y , z ) = ( 2 \sinh 2 z ) \mathbf { i } + \left( 4 e ^ { 4 z } \cos 4 y \right) \mathbf { j } + ( 4 x \cosh 2 z ) \mathbf { k }$$

---

Definitions:

Merchandise

Goods or products that are bought, sold, or traded in the retail environment.

Merchandise Inventory

Goods available for sale to customers, held by a business; categorized as a current asset on the balance sheet.

Purchase Discounts

Reductions in the amount owed by a buyer to a seller for goods purchased, typically gained by paying early or within a specified period.

Freight Costs

Expenses incurred by a company to transport goods, included in the cost of goods sold or recorded as an expense depending on the terms of delivery.