Use the Intermediate Value Theorem for Polynomials to Show That $$f ( x ) = 6 x ^ { 3 } - 10 x + 7 ; - 2 \text { and } - 1$$

question 103

Multiple Choice

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
- $$f ( x ) = 6 x ^ { 3 } - 10 x + 7 ; - 2 \text { and } - 1$$

• A) \(f ( - 2 ) = - 21\) and \(f ( - 1 ) = 11\)
• B) \(f ( - 2 ) = - 20\) and \(f ( - 1 ) = 12\)
• C) \(f ( - 2 ) = 21\) and \(f ( - 1 ) = - 11\)
• D) \(f ( - 2 ) = 21\) and \(f ( - 1 ) = 11\)

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Definitions:

Probability

The quantification of how probable it is for an event to take place, indicated by a value ranging from 0 to 1.

Strictly Convex Preferences

Strictly convex preferences indicate a consumer's increasing marginal rate of substitution, reflecting a stronger preference for balanced bundles of goods over extremes.

Risk Averse

A characteristic of a person or entity that prefers to avoid uncertainty and potentially negative outcomes, often opting for more certain or less risky options.

Risk Averse

Refers to the preference of avoiding risk rather than facing uncertainty or engaging in risky ventures.