Determine the T Intervals on Which the Curve $x = 6 t ^ { 2 } , y = t ^ { 3 } - 3 t \text { is concave }$

question 113

Multiple Choice

Determine the t intervals on which the curve $x = 6 t ^ { 2 } , y = t ^ { 3 } - 3 t \text { is concave }$ downward or concave upward.

• A) concave downward: \(- \infty < t < 0\); concave upward: \(0 < t < \infty\)
• B) concave downward: \(0 < t < \infty\); concave upward: \(- \infty < t < 0\)
• C) concave downward: \(- 6 < t < 3\); concave upward: \(0 < t < 3\)
• D) concave downward: \(- 6 < t < 0\); concave upward: \(0 < t < \infty\)
• E) concave downward: \(- \infty < t < 0\); concave upward: \(0 < t < 3\)

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Definitions:

Fixed Costs

Expenses that do not change in total despite fluctuations in production or sales levels, such as rent, salaries, and insurance premiums.

Break-Even Point

The point at which total costs and total revenue are equal, resulting in no net loss or gain, and where the business is essentially covering all its costs.

Contribution Margin Ratio

A measure of a company's ability to cover variable costs with sales, calculated as (Sales - Variable Costs)/Sales.

Fixed Costs

Expenditures on items like rent, salaries, and insurance that stay fixed, irrespective of production or sales figures.