Problem

For \(y~=~2\sqrt{t~-~1}~+~6\), where \(t~\ge~1\) is hours after opening and \(y\) is waiting time in minutes, find the endpoint, classify and interpret the global extremum, and state whether a global maximum exists.

Prompt context-labeled graph of y=2√(t−1)+6 with the endpoint visible and extremum conclusion withheld.

Answer choices

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Preview only

Endpoint: (1,6). Type: local minimum only. Context: 6 minutes at 1 hour is only a nearby low; both global extrema are claimed absent.

Endpoint: (1,6). Type: global minimum. Context: the least wait is 6 minutes at 1 hour; no global maximum exists because waiting time grows without bound.

Endpoint: (6,1). Type: global minimum. Context: the least wait is 1 minute at 6 hours; no global maximum exists because waiting time grows without bound.

Endpoint: (1,6). Type: global maximum. Context: the greatest wait is 6 minutes at 1 hour; no global minimum exists because waiting time decreases without bound.

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For \(y~=~2\sqrt{t~-~1}~+~6\), where \(t~\ge~1\) is hours after opening and \(y\) is waiting time in minutes, find the endpoint, classify and interpret the global extremum, and state whether a global maximum exists.

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