What's the longest past your due date your doctor will let you go?

I'm 36 + 3 today, and I went in my for last ultrasound. Baby boy is estimating at 7 lbs, which is making me nervous to have a big baby but my doctor doesn't seem concerned. I asked her if he hasn't come by my due date (7/30) how long past my due date would I go. She said at 41 weeks we would induce if he hasn't come. I sure hope he comes on his own though, he's in great birthing position she says but my cervix isn't doing anything lol.