Determine Where the Function Is Increasing and Where It Is $$f ( x ) = - 4 x ^ { 2 } - 2 x - 11$$

question 40

Multiple Choice

Determine where the function is increasing and where it is decreasing.
- $$f ( x ) = - 4 x ^ { 2 } - 2 x - 11$$

• A) increasing on \(\left( - \infty , - \frac { 1 } { 4 } \right)\)
• decreasing on \(\left( - \frac { 1 } { 4 } , \infty \right)\)
• B) increasing on \(\left( - \infty , \frac { 1 } { 4 } \right)\)
• decreasing on \(\left( \frac { 1 } { 4 } , \infty \right)\)
• C) decreasing on \(\left( - \infty , - \frac { 1 } { 4 } \right)\)
• increasing on \(\left( - \frac { 1 } { 4 } , \infty \right)\)
• D) increasing on \(\left( - \infty , - \frac { 43 } { 4 } \right)\)
• decreasing on \(\left( - \frac { 43 } { 4 } , \infty \right)\)

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Definitions:

Acetyl-CoA

A molecule that plays a key role in metabolism, serving as a building block for biosynthetic processes and involved in the cycle of energy production.

Citric Acid Cycle

A series of chemical reactions used by all aerobic organisms to release stored energy through the oxidation of acetyl-CoA derived from carbohydrates, fats, and proteins into carbon dioxide and chemical energy in the form of ATP.

Final Reaction

The last in a series of chemical reactions, often resulting in the formation of the desired product.

Citric Acid Cycle

The Citric Acid Cycle, also known as the Krebs cycle, is a series of chemical reactions used by all aerobic organisms to release stored energy through the oxidation of acetyl-CoA.