Using the Derivative of F(x) Given Below, Determine the Intervals $$f ^ { \prime } ( x ) = ( x - 5 ) e ^ { - x }$$

question 224

Multiple Choice

Using the derivative of f(x) given below, determine the intervals on which f(x) is increasing or decreasing.
- $$f ^ { \prime } ( x ) = ( x - 5 ) e ^ { - x }$$

• A) Decreasing on \(( - \infty , - 5 )\); increasing on \(( - 5 , \infty )\)
• B) Increasing on \(( - \infty , 5 )\); decreasing on \(( 5 , \infty )\)
• C) Increasing on \(( - \infty , - 5 )\); decreasing on \(( - 5 , \infty )\)
• D) Decreasing on \(( - \infty , 5 )\); increasing on \(( 5 , \infty )\)

---

Definitions:

Rationalizing

Rationalizing involves justifying actions or decisions, often in a way that avoids the true reasons or excuses behaviors.

Long-Term Self-Interests

Long-term self-interests are goals or desires that an individual seeks to achieve over an extended period, considering future well-being and success.

Individualism

A moral, political, or social outlook that emphasizes the moral worth of the individual and the priority of personal independence and rights.

Ethical Standards

The criteria that guide the behavior of individuals and organizations, reflecting what is morally right and wrong.