Improving your low range

There are two types of problems that crop up in flute playing that are low range problems: 1 - “I can't play low notes at all” 2 - “I can play low notes, but no one can hear them”
Problem #1 is the one I am going to address today.
It is often the case that beginner flutists will have the difficulty of not being able to produce low notes beyond a certain point. It always feels like you hit a hard line, and they just won't come out. Luckily, there IS a way to get through that roadblock, because it is often just a matter of your embouchure being set just a little bit different from other players, which makes high-range notes easier than low-range notes – trust me, all those flutists who can't hit the high notes are very jealous of you!
The key is usually in adjusting one of two things: your lips or your jaw. Put down your flute, and let's test it out with a couple of easy exercises.
First, without worrying about the shape of your lips (just make an “oooo” shape), alternate between blowing straight out in front of you, then blowing on your forehead (if you have bangs, they should fly up in the airstream), then blowing down on your chin. You should be able to do this by moving your bottom lip in and out (in to blow on your chin, and out for your forehead).
Once you have mastered that, put the palm of your hand about six inches in front of your face, and then lower it into a position as if it were a book (the top of your finger should be at your chin height – still 6 inches in front of you). You should be able to shape your flute embouchure and blow on the tips of your fingers. Once you feel the air on your fingertips (move your hand closer if it is difficult), begin moving your bottom lip out and in (as you did in the previous exercise), so that you move the airstream up and down your hand in a slow and controlled manner.
IMPORTANT! Remember what it feels like to point the airstream down!
Now, pick up your flute and play the lowest note that you are usually able to play. Finger the next lower note while you practice blowing your airstream more downward. It may also make a difference if you make your embouchure more relaxed (it can help to widen and soften your lips). Repeat your lowest “good” note, then slur to that newest lower note that you just tried. Do this several times!
Once you have that new note sounding better, keep slowly working your way down, slurring by half-steps until you reach the lowest note on your flute.
Now, there is a chance that you might still be having trouble moving down. The above exercise emphasizes an adjustment to your lips. However, you may need to move your jaw as well.
Put you flute down once again, and practice saying a long “eeeee” sound, and then changing to a long “ooooo” sound. Do this several times, to make sure that you can feel how you are moving your jaw forward with each “ooooo”, and back with each “eeeee”.
Now, put your flute up to your chin, in a regular playing position, with the same pressure against your chin that you have when playing. Practice saying the syllables again, so you get an idea of what it will feel like when you are really playing.
Now, find you lowest “good” note, and play and hold it this time. Now slur down a half-step, while changing your lips to look like more of an “eeee” shape. You embouchure will automatically get a little bit wider and flatter, while your jaw moves back just slightly. Think of nice warm air going through your flute at this point, and it should make it easier.
As above, if you are able to move down to that next lower note, repeat the slurring exercise, going down by half-steps while keeping your embouchure relaxed the whole time.
The half-step slurring exercise is an excellent warm-up for the low range, and I would recommend playing through those low notes whenever you begin your practice sessions, or just before band class, when everyone is playing and warming up. By playing those notes every day, you will improve how those notes sound, and slowly be able to make them clearer and stronger.