Solve the Problem $f ( x , y ) = x ^ { 2 } + x y + y ^ { 2 }$

question 83

Multiple Choice

Solve the problem.
-Find the derivative of the function $f ( x , y ) = x ^ { 2 } + x y + y ^ { 2 }$ at the point $( 4,5 )$ in the direction in which the function increases most rapidly.

• A) \(\sqrt { 293 }\)
• B) \(3 \sqrt { 42 }\)
• C) \(\sqrt { 299 }\)
• D) \(\sqrt { 365 }\)

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Definitions:

Contribution Format

An income statement format that separates fixed and variable costs, highlighting the contribution margin of products sold.

Sales Volume

The quantity of products or services sold within a specific period, not taking into account the sales price.

Unit Product Costs

The total cost associated with producing a single unit of product, including labor, materials, and overhead.

Variable Costing

An accounting method that only includes variable production costs in product costs, excluding fixed manufacturing overhead.