Identify the Open Intervals Where the Function $f ( x ) = x \sqrt { 24 - x ^ { 2 } }$

question 75

Multiple Choice

Identify the open intervals where the function $f ( x ) = x \sqrt { 24 - x ^ { 2 } }$ is increasing or decreasing.

• A)decreasing: \(( - \infty , \sqrt { 12 } )\) ; increasing: \(( \sqrt { 12 } , \infty )\)
• B)increasing: \(( - \sqrt { 12 } , \sqrt { 12 } )\) ; decreasing: \(( - \sqrt { 24 } , - \sqrt { 12 } ) \cup ( \sqrt { 12 } , \sqrt { 24 } )\)
• C)increasing: \(( - \infty , \sqrt { 24 } )\) ; decreasing: \(( \sqrt { 24 } , \infty )\)
• D)increasing: \(( - \sqrt { 24 } , - \sqrt { 12 } ) \cup ( \sqrt { 12 } , \sqrt { 24 } )\) ; decreasing: \(( - \sqrt { 12 } , \sqrt { 12 } )\)
• E)decreasing for all x

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Definitions:

Need-Based Theory

A motivational theory suggesting that behavior is driven by an individual's desire to fulfill unmet needs, ranging from basic survival needs to complex psychological needs.

Fixed Ratio Schedules

A reinforcement strategy in which a response is rewarded only after a specified number of responses, used in various contexts, including behavioral psychology.

Reinforcement Theory

A theory in psychology that suggests behavior is motivated by its consequences, with reinforcement used to increase or decrease specific behaviors.

Behavior

The actions or reactions of an individual or system in response to external or internal stimuli.