Use the Intermediate Value Theorem to Determine Whether the Polynomial $$f ( x ) = - 6 x ^ { 4 } - 3 x ^ { 2 } + 6 ; [ - 1,0 ]$$

question 170

Multiple Choice

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
- $$f ( x ) = - 6 x ^ { 4 } - 3 x ^ { 2 } + 6 ; [ - 1,0 ]$$

• A) \(f ( - 1 ) = 3\) and \(f ( 0 ) = 7\); no
• B) \(f ( - 1 ) = - 3\) and \(f ( 0 ) = - 6\); no
• C) \(f ( - 1 ) = 3\) and \(f ( 0 ) = - 6\); yes
• D) \(f ( - 1 ) = - 3\) and \(f ( 0 ) = 6\); yes

---

Definitions:

Fixed Inputs

Resources in production that remain constant in quantity regardless of the level of output or activity.

Variable Inputs

Resources used in production that vary with the level of output, such as raw materials.

Short-Run

A period of time in economics where at least one input is fixed, limiting the ability to fully adjust to market changes.

Gasoline Costs

Expenses related to the purchase of gasoline, often significant for individuals and businesses relying on transportation.