Find All Possible Functions with the Given Derivative $y ^ { \prime } = x ^ { 3 } - 8 x$

question 230

Multiple Choice

Find all possible functions with the given derivative.
- $y ^ { \prime } = x ^ { 3 } - 8 x$

• A) \(\frac { x ^ { 4 } } { 4 } - \frac { 8 x ^ { 2 } } { 2 } + C\)
• B) \(\frac { x ^ { 4 } } { 4 } + 8 x ^ { 2 } + C\)
• C) \(\frac { x ^ { 3 } } { 3 } - \frac { 8 x ^ { 2 } } { 2 } + C\)
• D) \(3 x ^ { 2 } - 8 + C\)

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Definitions:

Binding Price Floor

A government or regulatory-imposed price control set above the equilibrium price, which prevents the market price from falling below that level.

Potential Sellers

Potential sellers are individuals or entities that may be willing to sell goods or services under the right conditions.

Price Floor

A government-imposed minimum price charged on a product, below which it cannot be sold to prevent market prices from falling too low.

Surplus

An excess of revenues over expenses in a budget, or an excess of goods or materials than what is needed.