Verify That the Function Satisfies the Three Hypotheses of Rolle's $f(x)=\sin 5 \pi x$

question 158

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) None of these
• 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) \(c_{1}=\pm \frac{1}{10}\) , \(c_{2}=\pm \frac{3}{10}\)

---

Definitions:

Nurturers

Individuals who provide care and support, fostering growth and development in others.

Household Roles

The functions and responsibilities assigned to different members of a family or household unit, often based on age, gender, or relationship.

Early Educators

Professionals specializing in the educational and developmental needs of young children, from infancy through the early elementary years.

Gender Specific Roles

Social and cultural expectations that dictate certain behaviors and responsibilities based on one's gender.