Use the Graph of the Function F(x) to Locate the Local

question 322

Multiple Choice

Use the graph of the function f(x) to locate the local extrema and identify the intervals where the function is concave up
and concave down.
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• A) Local minimum at \(x = 2\); local maximum at \(x = 0\); concave down on \(( 0 , \infty )\); concave up on \(( \infty , 0 )\)
• B) Local minimum at \(x = 2\); local maximum at \(x = 0\); concave up on \(( 0 , \infty )\); concave down on \(( - \infty , 0 )\)
• C) Local minimum at \(x = 0\); local maximum at \(x = 2\); concave up on \(( 0 , \infty )\); concave down on \(( - \infty , 0 )\)
• D) Local minimum at \(x = 0\); local maximum at \(x = 2\); concave down on \(( 0 , \infty )\); concave up on \(( - \infty , 0 )\)

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Definitions:

Sleeping Clusters

Groups of animals that gather and sleep together for mutual benefits such as warmth, protection from predators, or social bonding.

Selfish Herd Hypothesis

A theory suggesting that individuals in a group move towards the center to reduce their predation risk, acting out of self-interest.

Sleeping Clusters

Groups formed by individuals of certain species during rest periods for protection or thermoregulation.

Assassin Bug

A member of the Reduviidae family of insects known for their predatory behavior, using a long rostrum to inject lethal saliva into their prey.