Find the Derivative of the Function Using the Definition of Derivative

question 167

Multiple Choice

Find the derivative of the function using the definition of derivative.
- $$f ( x ) = x ^ { 3 } + 5 x$$

• A) \(f ^ { \prime } ( x ) = x ^ { 2 } + 5\)
• B) \(f ^ { \prime } ( x ) = 3 x ^ { 2 } + 5 x\)
• C) \(f ^ { \prime } ( x ) = 3 x ^ { 2 }\)
• D) \(f ^ { \prime } ( x ) = 3 x ^ { 2 } + 5\)

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Definitions:

Externalities

Financial outcomes or repercussions that impact third parties who are not directly involved; these can be positive or negative.

Invisible Hand

A term coined by Adam Smith to describe the self-regulating nature of the marketplace in adjusting supply and demand autonomously.

Marketplace

A physical or digital venue where buyers and sellers come together to exchange goods, services, or information.

Marginal Buyer

The consumer who might leave the market if the price was any higher, indicating their participation is sensitive to price changes.