Use the Intermediate Value Theorem to Determine Whether the Polynomial $$f ( x ) = - 9 x ^ { 4 } + 2 x ^ { 3 } + 8 x + 1 ; [ 1,2 ]$$

question 301

Multiple Choice

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
- $$f ( x ) = - 9 x ^ { 4 } + 2 x ^ { 3 } + 8 x + 1 ; [ 1,2 ]$$

• A) \(f ( 1 ) = 2\) and \(f ( 2 ) = - 111\); yes
• B) \(f ( 1 ) = 2\) and \(f ( 2 ) = 111\); no
• C) \(f ( 1 ) = - 2\) and \(f ( 2 ) = 111\); yes
• D) \(f ( 1 ) = - 2\) and \(f ( 2 ) = - 111\); no

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Definitions:

Standardized Test Statistic

A test statistic that has been transformed to have no units or scaling, facilitating comparison across different datasets or studies.

Null Hypothesis

A statement or proposition that specifies no effect or no difference and that researchers aim to test.

Level Of Significance

The probability of incorrectly rejecting a true null hypothesis, often denoted by alpha in hypothesis testing.

Confidence Interval

A range of values, derived from sample statistics, that is likely to contain the population parameter with a specified level of confidence.