its at the end of the bat

one inch from the end of the bat to where it narrows

The ball will definitely go farther if hit off the "sweet spot," and it will feel "sweet" to your hands due to the shock from impact being reduced to practically nothing while the ball goes farther.

Once you find the spot on your bat, mark it with tape or something of the sort, and practice hitting off a tee to perfect your mechanics and sweet spot hitting.

If you think the tee is a waste of time or only for super young kids, watch what Tony Gwynn thinks about the tee:

http://www.youthfitnessmag.com/quick-tips-tony-gwynn-jr

near the end of your bat

Start by holding the bat horizontal in one hand. Grab a ball and just bounce it off the bat starting at the handle end working toward the barrel plug end. you will hear and see a difference in the sound and bounce back of the ball at the sweet spot. Most youth bats have about a 3" sweet spot but that will vary with wooden bats and complex construction aluminum alloy bats.

A bit after were the small part is done getting bigger.

you will feel it when you hit it

in the middle on your bat

I recently went to the Museum of Science in Boston and they had a lecture about
baseball. They took a piece of regular paper and wrapped it around the handle of
the bat and taped it so a cone was created and the inside of the cone touched the
knub of the bat. While one person holds the bat head down with two fingers another
person hits the bat with a knuckle or some other object. As you move up and down
the bat you will hear the paper buzz from vibration. Eventually you will find a spot
where the paper does not buzz and that is the sweet spot.