How to play lower notes on alto saxophone?

Notes like low F, E, and D. My primary instrument is clarinet. I started playing the alto sax almost a year ago and it's difficult for me to play low notes. I loosen my jaw and don't movie my upper lip/mouth move down the mouthpiece like my instructor advised me, but it's still hard for me to play. Especially in fast transitions (namely the guitar solo in Crazy Train ;) ) any advice?