Verify That the Function Satisfies the Three Hypotheses of Rolle's $$f ( x ) = \sin 5 \pi x , \left[ - \frac { 2 } { 5 } , \frac { 2 } { 5 } \right]$$

question 30

Multiple Choice

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. $$f ( x ) = \sin 5 \pi x , \left[ - \frac { 2 } { 5 } , \frac { 2 } { 5 } \right]$$

• A) \(c _ { 1 } = \pm \frac { 1 } { 10 } , c _ { 2 } = \pm \frac { 3 } { 10 }\)
• B) \(c _ { 1 } = \pm \frac { 1 } { 10 } , c _ { 2 } = \frac { 3 } { 10 }\)
• C) \(c _ { 1 } = - \frac { 1 } { 10 } , c _ { 2 } = \pm \frac { 1 } { 10 }\)
• D) \(c _ { 1 } = \frac { 1 } { 10 } , c _ { 2 } = \pm \frac { 3 } { 10 }\)
• E) None of these

---

Definitions:

Moral Obligation

A duty or commitment to act in a way that is considered morally correct by societal standards.

Frequent Praise

Regularly expressing approval or admiration to reinforce positive behavior and motivate individuals or groups.

ERG Theory

A motivational theory developed by Clayton Alderfer that categorizes human needs into three groups: Existence, Relatedness, and Growth.

Three Stages

A conceptual division of a process or phenomenon into three sequential phases for easier understanding and analysis.