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 \(x = 3\)

---

Definitions:

Fentanyl

A potent synthetic opioid analgesic used for severe pain management, but associated with a high risk of overdose and addiction.

Midazolam (Versed)

A medication commonly used for sedation, anxiolysis, or anesthesia before medical procedures.

Débridement

The medical removal of dead, damaged, or infected tissue to improve the healing potential of the remaining healthy tissue.

Pain Relief

Methods or treatments used to reduce or alleviate discomfort and pain, ranging from medication to physical therapies.