You can separate two tangent handles (“break” the tangent) and move them separately using the Break option from the Edit Mode box:

• To break and move a tangent handle, select Break and click the tangent handle. The tangent is displayed as a solid line, indicating it is “broken.”
• To reconnect two broken tangent handles, select Auto and click either of the two tangent handles. The tangent is displayed as a dotted line.
• To change the position of an individual tangent handle after releasing the cursor, select Move.