Use the Derivative Of $f ( x ) = 5 x ^ { 3 } + 15 x$

question 117

Multiple Choice

Use the derivative of $f ( x ) = 5 x ^ { 3 } + 15 x$ to determine any points on the graph of $f ( x )$ at which the tangent line is horizontal.

• A) \(( 1,20 )\)
• B) \(( 1,20 )\) and \(( - 1 , - 20 )\)
• C) \(( 5,700 )\) and \(( - 5,700 )\)
• D) \(( 0,0 )\)
• E) \(f ( x )\) has no points with a horizontal tangent line.

---

Definitions:

Financial Services

Refers to economic services provided by the finance industry, including banks, credit unions, and insurance companies, encompassing a broad range of money management activities.

Manufacturing Sector

A sector of the economy that is involved in the production of goods through the processing of raw materials and assembly of components.

Production

The process of creating, manufacturing, or generating goods and services, often measured in terms of output or efficiency in an economic context.

Motorcycles

Two-wheeled vehicles that are powered by an engine, often used for transportation, recreation, or sport.