Use the Intermediate Value Theorem for Polynomials to Show That $f ( x ) = 7 x ^ { 3 } + 9 x ^ { 2 } - 7 x + 4 ; - 2$

question 58

Multiple Choice

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
- $f ( x ) = 7 x ^ { 3 } + 9 x ^ { 2 } - 7 x + 4 ; - 2$ and $- 1$

• A) \(f ( - 2 ) = - 2\) and \(f ( - 1 ) = 13\)
• B) \(f ( - 2 ) = 2\) and \(f ( - 1 ) = - 13\)
• C) \(f ( - 2 ) = - 1\) and \(f ( - 1 ) = 14\)
• D) \(f ( - 2 ) = 2\) and \(f ( - 1 ) = 13\)

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Definitions:

Modality

Value or values of a variable that have the highest frequency in a set of data.

Directional Hypothesis

A specific type of hypothesis that stipulates the direction of the expected relationship between variables (e.g., 'greater than', 'less than').

Non-directional Hypothesis

A hypothesis that predicts a relationship between variables without specifying the direction of the relationship.

Two-tailed

Involves hypotheses testing that considers both directions of differences (greater than or less than) without specifying which direction.