Day 1: paclitaxel 175 mg/m2 over 3 hours followed by carboplatin AUC 5 (AUC 5 is a term used to describe the dosing of carboplatin based on a patient's height, weight and kidney function) over 45 minutes Days 1-14: axitinib 5 mg PO twice daily Days 15-21: break from treatment Arm A: FLT PET cohort subjects will have FLT PET scans up to 2 weeks prior to day 1 and on days 14, 17, and 21 of cycle 1.