On the Same Coordinate Axes, Sketch the Graphs (As Accurately $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - x + 3$

question 130

Essay

On the same coordinate axes, sketch the graphs (as accurately as possible) of the functions $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - x + 3$ and $g ( x ) = - 4 x ^ { 2 } + 3 x + 3$ . Based on your sketch, how many points do the graphs appear to intersect? Find the coordinates of all intersection points.

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Definitions:

Contribution Margin

The difference between sales revenue and variable costs, indicating how much revenue contributes to covering fixed costs and profit generation.

Fixed Costs

Expenses that do not vary with the level of production or sales, such as rent, salaries, and insurance.

Operating Income

Earnings before interest and taxes (EBIT), a measure of a company's profitability from its core operations.

Direct Labor Efficiency Variance

A financial metric that analyzes the difference between the actual hours worked and the standard hours expected for the production achieved.