Identify the Function's Extreme Values in the Given Domain, and Say

question 101

Multiple Choice

Identify the function's extreme values in the given domain, and say where they are assumed. Tell which of the extreme
values, if any, are absolute.
- $$g ( t ) = \frac { t ^ { 3 } } { 3 } - \frac { 11 } { 2 } t ^ { 2 } + 24 t , 0 \leq t < \infty$$

• A) local minimum: \(\frac { 63 } { 2 }\) at \(x = 3\); local maximum: 0 at \(x = 0\); absolute maximum: \(\frac { 32 } { 3 }\) at \(x = 8\)
• B) local minimum: \(\frac { 63 } { 2 }\) at \(x = 3\); local and absolute maximum: \(\frac { 32 } { 3 }\) at \(x = 8\)
• C) local minimum: 0 at \(x = 0\); local and absolute minimum: \(\frac { 32 } { 3 }\) at \(x = 8\); local maximum: \(\frac { 63 } { 2 }\) at \(x = 3\)
• D) local and absolute minimum: \(\frac { 32 } { 3 }\) at \(x = 8\); local maximum: \(\frac { 63 } { 2 }\) at \(x = 3\)

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