Verify That the Function Satisfies the Three Hypotheses of Rolle's $c$

question 132

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:

Social Trap

Situations in which actions that produce rewards for one individual or group in the short term lead to negative consequences for all in the long term.

Fuel-Inefficient Car

A vehicle that consumes a high amount of fuel relative to the distance it travels, reflecting poor energy efficiency.

Greenhouse Gases

Gases in Earth's atmosphere that trap heat, such as carbon dioxide and methane, contributing to global warming and climate change.

Bystander Effect

An occurrence in social psychology where the presence of others decreases an individual's likelihood to aid someone in need.