Determine Where the Function Is Increasing and Where It Is $$f ( x ) = - x ^ { 2 } + 2 x + 8$$

question 11

Multiple Choice

Determine where the function is increasing and where it is decreasing.
- $$f ( x ) = - x ^ { 2 } + 2 x + 8$$

• A) increasing on \(( - \infty , 1 )\)
• decreasing on \(( 1 , \infty )\)
• B) increasing on \(( 9 , \infty )\)
• decreasing on \(( - \infty , 9 )\)
• C) increasing on \(( 1 , \infty )\)
• decreasing on \(( - \infty , 1 )\)
• D) increasing on \(( - \infty , 9 )\)
• decreasing on \(( 9 , \infty )\)

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Definitions:

π Network

A system of conjugated pi bonds within a molecule that allows for the delocalization of pi electrons across all the adjacent aligned p orbitals.

Extremely Slow Rate

Describes a process or reaction that proceeds at a very slow pace, often due to kinetic barriers or unfavorable conditions.

3-Chlorocyclopropene

A halogenated organic compound involving a three-membered ring structure with one chlorine atom attached.

Solvolyzed

Refers to a chemical compound that has undergone solvolysis, a reaction where the solvent participates and changes the compound, often by breaking bonds.