Use a Graphing Utility to Graph the Function and Visually $f ( x ) = - x ^ { 3 } + 3 x + 1$

question 76

Multiple Choice

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant.
$f ( x ) = - x ^ { 3 } + 3 x + 1$

• A) increasing on \(( - \infty , - 1 )\)
• decreasing on \(( - 1,1 )\)
• increasing on \(( 1 , \infty )\)
• B) decreasing on \(( - \infty , 0 )\)
• increasing on \(( 0 , \infty )\)
• C) decreasing on \(( - \infty , \infty )\)
• D) increasing on \(( - \infty , \infty )\)
• E) decreasing on \(( - \infty , - 1 )\)
• increasing on \(( - 1,1 )\)
• decreasing on \(( 1 , \infty )\)

---

Definitions:

Barbiturates

A class of drugs derived from barbituric acid, used as sedatives, hypnotics, and anticonvulsants, but known for potential abuse and addiction.

Intravenously

The administration of liquid substances directly into a vein, commonly used for medication or nutritional delivery in medical settings.

Mental Capacity

The ability of an individual to make decisions or perform tasks that require cognitive functions such as understanding, reasoning, and remembering.

Technical Means

Tools, equipment, and procedures used in the production of goods and services.