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:

Normal Good

A type of good for which demand increases as the income of individuals increases, holding everything else constant.

Wage Rate

The standard amount of compensation given to employees for services rendered, usually expressed per hour or year.

Second Job

An additional employment undertaken by an individual besides their primary job to earn extra income or explore a different field.

Net Seller

An entity or individual that sells more of a security, commodity, or product than is purchased over a specific time period.