$\text { Locate the absolute extrema of the function } g ( t ) = \frac { t ^ { 2 } } { t ^ { 2 } + 2 } \text { on the closed interval }$

question 99

Multiple Choice

$\text { Locate the absolute extrema of the function } g ( t ) = \frac { t ^ { 2 } } { t ^ { 2 } + 2 } \text { on the closed interval }$ $[ - 3,3 ] \text {. }$

• A) The absolute maximum is \(\frac { 9 } { 11 }\), and it occurs at the critical number \(x = 0\).
• The absolute minimum is \(\frac { 9 } { 5 }\), and it occurs at the left endpoint \(x = - 3\).
• B) The absolute maximum is \(\frac { 9 } { 11 }\), and it occurs at either endpoint \(x = \pm 3\).
• The absolute minimum is 0 , and it occurs at the critical number \(x = 0\).
• C) The absolute maximum is \(\frac { 9 } { 11 }\), and it occurs only at the left endpoint \(x = - 3\).
• The absolute minimum is 0 and it occurs at the critical number \(x = 0\).
• D) The absolute maximum is \(\frac { 9 } { 11 }\), and it occurs at the critical number \(x = 0\).
• The absolute minimum is \(\frac { 9 } { 5 }\), and it occurs at the right endpoint \(x = 3\).
• E) The absolute maximum is \(\frac { 9 } { 11 }\), and it occurs only at the right endpoint \(x = 3\) The absolute minimum is 0 and it occurs at the critical number \(x = 0\).

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