Using the Derivative of F(x) Given Below, Determine the Intervals $$f ^ { \prime } ( x ) = ( 1 - x ) ( 9 - x )$$

question 314

Multiple Choice

Using the derivative of f(x) given below, determine the intervals on which f(x) is increasing or decreasing.
- $$f ^ { \prime } ( x ) = ( 1 - x ) ( 9 - x )$$

• A) Decreasing on \(( - \infty , - 1 ) \cup ( - 9 , \infty )\); increasing on \(( - 1 , - 9 )\)
• B) Decreasing on \(( - \infty , 1 ) \cup ( 9 , \infty )\); increasing on \(( 1,9 )\)
• C) Decreasing on \(( 1,9 )\); increasing on \(( - \infty , 1 ) \cup ( 9 , \infty )\)
• D) Decreasing on \(( - \infty , 1 )\); increasing on \(( 9 , \infty )\)

---

Definitions:

Acetyl CoA

Acetyl CoA is a central metabolite in energy metabolism, acting as a substrate for the citric acid cycle and involved in the synthesis and oxidation of fatty acids.

Citric Acid Cycle

A sequence of biochemical processes that all oxygen-using organisms employ to produce energy by converting acetate, obtained from carbohydrates, fats, and proteins, into carbon dioxide.

Acetyl Group

A 2-carbon group derived from acetic acid (acetate).

FADH₂

A reduced form of flavin adenine dinucleotide, a redox-active coenzyme involved in cellular respiration.