Find the Derivative at Each Critical Point and Determine the Local

question 150

Multiple Choice

Find the derivative at each critical point and determine the local extreme values.
- $y = x \left( 4 - x ^ { 2 } \right)$

• A)
• \(\begin{array}{l|l|l|r}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=-1.15 & 0 & \text { local max } & 3.08 \\
• x=1.15 & 0 & \text { local min } & -6.16
• \end{array}\)
• B)
• \(\begin{array}{l|l|l|r}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=1.15 & 0 & \text { local max } & 3.08 \\
• x=-1.15 & 0 & \text { local min } & -3.08
• \end{array}\)
• C)
• \(\begin{array}{c|l|l|c}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline x=-1.15 & 0 & \text { local max } & -6.16 \\
• x=1.15 & 0 & \text { local min } & 3.08
• \end{array}\)
• D)
• \(\begin{array}{l|l|l|r}
• \text { Critical Pt. } & \text { derivative } & \text { Extremum } & \text { Value } \\
• \hline \mathrm{x}=1.15 & 0 & \text { local max } & -6.16 \\
• \mathrm{x}=-1.15 & 0 & \text { local min } & 3.08
• \end{array}\)

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Definitions:

Optimal Consumption Bundle

The blend of items and services that enhances a buyer's fulfillment to the fullest within their spending ability.

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A combination of goods and services that a consumer chooses to consume within a given time period.

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Funds acquired regularly as earnings from employment or investment returns.

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The change in consumption patterns due to a change in relative prices, holding the consumer's utility level constant.