Find the Point on the Curve Given Below at Which $$y = 10 x ^ { 3 } + 31 x ^ { 2 } + 5 x$$

question 58

Multiple Choice

Find the point on the curve given below at which the curvature K is zero. $$y = 10 x ^ { 3 } + 31 x ^ { 2 } + 5 x$$

• A) \(x = \frac { 30 } { 31 }\)
• B) \(x = \frac { 31 } { 30 }\)
• C)\(x = - \frac { 31 } { 30 }\)
• D)\(x = - \frac { 30 } { 31 }\)
• E)\(x = - \frac { 31 } { 10 }\)

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Definitions:

Equilibrium Output

The level of output where the quantity of goods produced equals the quantity of goods consumed, and the market is in balance.

Total Revenues

The full revenue obtained from the sale of goods or services, before taking out any expenditures.

Long-Run Equilibrium

Long-run equilibrium occurs when all factors of production within a market are fully adjusted to the economic conditions, leading to a steady state where there is no tendency for change.

Consumer Surpluses

The difference between the total amount that consumers are willing to pay and the total amount that they actually pay for a good or service.