**Core Concept**
Pseudomonas aeruginosa is a Gram-negative bacterium known for its resistance to multiple antibiotics, often due to the production of extended-spectrum beta-lactamases (ESBLs) or other beta-lactamases. In cases of febrile neutropenia, effective antibiotic therapy is crucial to prevent further complications.

**Why the Correct Answer is Right**
The production of ESBLs in Pseudomonas aeruginosa confers resistance to most beta-lactam antibiotics, including penicillins and cephalosporins. In this scenario, the use of carbapenems, such as meropenem, is recommended due to their stability against ESBLs. Carbapenems inhibit bacterial cell wall synthesis by binding to penicillin-binding proteins (PBPs), ultimately leading to bacterial cell death.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect as the use of aminoglycosides, such as gentamicin, would not be the best choice due to potential nephrotoxicity and ototoxicity, especially in patients with compromised renal function.
**Option B:** This option is incorrect as fluoroquinolones, such as ciprofloxacin, may not be effective against Pseudomonas aeruginosa, particularly in the setting of febrile neutropenia where prompt and effective therapy is essential.
**Option C:** This option is incorrect as the use of tigecycline, a glycylcycline antibiotic, may not be the most effective option due to its limited spectrum of activity against Pseudomonas aeruginosa.

**Clinical Pearl / High-Yield Fact**
In febrile neutropenia, the use of carbapenems, such as meropenem, should be considered early in the treatment course, especially in cases where ESBL-producing bacteria are suspected. This can help prevent further complications and improve patient outcomes.

**Correct Answer:** C. Meropenem