Use the Intermediate Value Theorem to Determine Whether the Polynomial $f ( x ) = 6 x ^ { 5 } - 7 x ^ { 3 } + 6 x ^ { 2 } - 2$

question 166

Multiple Choice

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given
integers
- $f ( x ) = 6 x ^ { 5 } - 7 x ^ { 3 } + 6 x ^ { 2 } - 2$ ; between $- 2$ and $- 1$

• A) \(f ( - 2 ) = - 114\) and \(f ( - 1 ) = - 5\); no
• B) \(f ( - 2 ) = - 114\) and \(f ( - 1 ) = 5\); yes
• C) \(f ( - 2 ) = 114\) and \(f ( - 1 ) = - 5\); yes
• D) \(f ( - 2 ) = 114\) and \(f ( - 1 ) = 5\); no

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Definitions:

Progressive Tax

A tax system in which the tax rate increases as the taxable amount increases, thereby imposing a higher percentage rate on higher-income earners.

High-Income

Earning a substantial amount of money, typically above the median income level in a given region or country.

Low-Income

Referring to individuals or families whose earnings are significantly lower than the average, often quantified by government standards.

Regressive Tax

A tax imposed in such a manner that the tax rate decreases as the amount subject to taxation increases.