**Core Concept**
The question is testing the ability to identify a drug that can be administered through multiple routes, which is an essential aspect of pharmacology in clinical practice. This requires knowledge of the physical and chemical properties of the drug, as well as its formulation and stability.

**Why the Correct Answer is Right**
The correct answer is **Fentanyl**, a potent opioid analgesic. Fentanyl can be administered through various routes due to its lipophilic nature, which allows it to cross biological membranes easily. Its intravenous (IV) formulation is commonly used for pain management and anesthesia. Fentanyl can also be administered epidurally for postoperative pain relief, where it is absorbed into the cerebrospinal fluid to provide analgesia. Additionally, transdermal patches containing fentanyl are available for chronic pain management, allowing for controlled release of the drug through the skin.

**Why Each Wrong Option is Incorrect**
**Option A:** Morphine is primarily administered orally or intravenously, but not commonly by epidural or transdermal routes due to its hydrophilic nature and potential for histamine release.
**Option B:** Diazepam is typically administered orally or intravenously, but its lipid solubility is not sufficient for effective transdermal absorption.
**Option C:** Midazolam is commonly used intravenously for sedation and anesthesia, but its pharmacokinetic profile is not suitable for epidural or transdermal administration.

**Clinical Pearl / High-Yield Fact**
Fentanyl's high lipophilicity allows it to cross the blood-brain barrier rapidly, making it a potent analgesic with a rapid onset of action. This property also increases its potential for abuse and overdose.

**Correct Answer: C. Fentanyl.**