Use the Intermediate Value Theorem for Polynomials to Show That $f ( x ) = 8 x ^ { 3 } + 9 x ^ { 2 } - 8 x - 5 ; - 2$

question 264

Multiple Choice

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
- $f ( x ) = 8 x ^ { 3 } + 9 x ^ { 2 } - 8 x - 5 ; - 2$ and $- 1$

• A) \(f ( - 2 ) = 17\) and \(f ( - 1 ) = - 4\)
• B) \(f ( - 2 ) = - 16\) and \(f ( - 1 ) = 5\)
• C) \(f ( - 2 ) = - 17\) and \(f ( - 1 ) = 4\)
• D) \(f ( - 2 ) = 17\) and \(f ( - 1 ) = 4\)

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Definitions:

Meninx

A term referring to any of the three membranes that cover the brain and spinal cord, including the dura mater, arachnoid mater, and pia mater.

Epidural Space

The area between the dura mater and the vertebral wall, containing fat and small blood vessels, often targeted for epidural anaesthesia.

Dura Mater

The outermost and toughest layer of the three membranes (meninges) that cover the brain and spinal cord.

Anesthesia

Anesthesia refers to a range of procedures that are used to prevent pain during surgery, which can be either local, regional, or general.