$f _ { y } ( x , y ) = 0$

question 10

Multiple Choice

$\text { For } f ( x , y ) = 17 x ^ { 3 } - 12 x y + y ^ { 3 } \text { find all values of } x \text { and } y \text { such that } f _ { x } ( x , y ) = 0 \text { and }$ $f _ { y } ( x , y ) = 0$ simultaneously.

• A) \(( 0,0 ) , \left( - \frac { 4 } { 17 ^ { 2 / 3 } } , - \frac { 4 } { 17 ^ { 1 / 3 } } \right)\)
• B) \(( 0,0 ) , \left( \frac { 4 } { 17 ^ { 2 / 3 } } , \frac { 4 } { 17 ^ { 1 / 3 } } \right)\)
• C)\(( 0,0 ) , \left( - \frac { 4 } { 17 ^ { 1 / 3 } } , \frac { 4 } { 17 ^ { 1 / 3 } } \right)\)
• D)\(( 0,0 ) , \left( - \frac { 4 } { 17 ^ { 1 / 3 } } , - \frac { 4 } { 17 ^ { 1 / 3 } } \right)\)
• E)\(( 0,0 ) , \left( \frac { 4 } { 17 ^ { 1 / 3 } } , - \frac { 4 } { 17 ^ { 1 / 3 } } \right)\)

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Definitions:

Net Profit

Net profit, also known as net income, is the amount of earnings remaining after all expenses, taxes, and costs have been subtracted from total revenues.

Variable Costs

Costs that vary in direct proportion to changes in the level of activity or production volume.

Breakeven Equation

A calculation representing the point at which total costs equal total revenue, indicating that a business neither makes profit nor incurs loss.

Selling Price

The amount at which a product or service is sold to customers, determined by factors like cost, demand, and market competition.