Let $f ( x , y ) = k x ^ { 3 } - 3 k x + y ^ { 2 }$

question 68

Essay

Let $f ( x , y ) = k x ^ { 3 } - 3 k x + y ^ { 2 }$ where k $\neq$ 0.Find the critical points of f.

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Definitions:

Break-even Sales

The amount of revenue needed to cover both the variable and fixed costs of a business, resulting in zero profit or loss.

Variable Cost

Costs that vary directly with the level of production or service delivery, such as raw materials and labor costs.

Fixed Costs

Costs that do not vary with the level of production or sales volume, remaining constant even as production levels change.

Break-even Point

The point at which total costs equal total revenue, resulting in no net loss or gain for the business.