Which of the following clinical signs would necessitate the administration of naloxone (Narcan)?

The administration of naloxone (Narcan) is indicated primarily in cases of opioid overdose. One of the hallmark clinical signs of opioid toxicity is slow or shallow respirations, which is referred to as respiratory depression. When opioids bind to the receptors in the brain responsible for controlling respiration, they can significantly decrease the rate and depth of breathing, leading to inadequate oxygen supply and potential respiratory failure.

In the context of this question, slow respirations would be a clear indicator of possible opioid involvement. The rapid identification and administration of naloxone would help to reverse the effects of opioids, restore normal respiratory function, and prevent further complications or death due to hypoxia.

The other signs, such as extreme agitation, tachycardia, and hypertension, are not directly linked to opioid overdose and may not indicate a need for naloxone. These symptoms can be associated with other conditions or substances, such as stimulants, anxiety states, or other medical issues. Therefore, they do not warrant the administration of naloxone as a front-line treatment.