Determine Whether Rolle's Theorem Can Be Applied to the Function $f ( x ) = \cos \pi x \text { on }$

question 36

Multiple Choice

Determine whether Rolle's Theorem can be applied to the function $f ( x ) = \cos \pi x \text { on }$ the closed interval $\left[ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right]$ . If Rolle's Theorem can be applied, find all numbers $c$ in the open interval $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ such that $f ^ { t } ( c ) = 0$ .

• A) Rolle's Theorem applies; \(c = 0\)
• B) Rolle's Theorem applies; \(c = - \frac { 1 } { 4 } , \frac { 1 } { 4 }\)
• C) Rolle's Theorem applies; \(c = 0 , - \frac { 1 } { 4 } , \frac { 1 } { 4 }\)
• D) Rolle's Theorem applies; \(c = \frac { 1 } { 4 }\)
• E) Rolle's Theorem does not apply.

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Definitions:

Variable Overhead Rate

Variable overhead rate is the cost of variable overhead (expenses that change with the level of production) allocated per unit of production activity, such as labor-hours or machine-hours.

Direct Labor-Hours

The total hours worked by employees who are directly involved in the manufacturing process or production of goods.

Fixed Manufacturing Overhead

Indirect manufacturing costs that remain constant regardless of the level of production, such as factory rent and salaries of production supervisors.

Variable Overhead Rate

This rate is used to apply the variable overhead costs to production activities, based on an activity base.