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

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Definitions:

Inverse Demand

A representation of demand that shows how the price of a good or service can vary inversely with changes in the quantity demanded.

Typeset

The composition of text by arranging physical or digital type to make written language legible, readable, and appealing when displayed.

Marginal Cost

The financial outlay required to produce an additional unit of a product or service.

Demand Curve

A graphical representation of the relationship between the price of a good and the quantity of the good that consumers are willing to buy.