1: Direct Select Tool Adjustment

Start off with a simple path like below. I used the pencil tool to make a simple curved line, and applied a brush stroke. I’ll start by showing you an adjustment with the Direct Select tool (white arrow) as a contrast/comparison.

Now lets say you want to adjust this shape, and you use the Direct Select tool (white arrow) and move the far right point where you want it like this:

And this is what you get. Ok, but you still might have to manually adjust the rest of the points to get what you’re looking for.

2: Reshape Tool Adjustment

Start with the same simple path (or a new one).

Now select your shape with the Selection tool (black arrow), and then select the Reshape tool.

Important: You need to have all points in your shape selected before you move the single point. If you only select a single anchor point before you use the Reshape tool, it will only adjust the path up to the next non-selected point (like the example above)

Ok, with all points on your path highlighted, move the far-right point with the Reshape tool, and you’ll notice a more natural adjustment.

In my opinion, this is a much more pleasing result:

One More Thing:

If you hold Option (Alt PC) while you drag with the Reshape tool, you can easily make copies of your shape that might prove to be useful. (almost like a manual blend tool).