Tesla stock fell early Tuesday, following Monday's big jump in the shares. Investors might be thinking about how well the company's cars drive themselves following Sunday's successful robo-taxi service launch.

Regulators are likely to do the same. The answer could result in some stock volatility.

Shares of the electric-vehicle maker were down 1.3% at $344.11.

Shares jumped 8.2% on Monday, getting a big boost from the robo-taxi service that Tesla opened on Sunday afternoon in Austin, Texas, as expected. It charged handpicked riders a flat fee of $4.20 per ride.

While a lot of videos circulated on X showing impressed riders giving positive reviews, eventually, some problems surfaced. One video posted by Rob Maurer showed a Tesla speeding, slightly, in a 35-mph zone. It struggled with a left turn, ending up in the lane for oncoming traffic for a few seconds. No cars were approaching.

To be sure, it was an error. Eventually "there's going to be some type of accident ...whether it's Tesla's fault or not," said Edward Jones analyst Jeff Windau, adding it will take time to see how Tesla's record develops.

He rates Tesla shares Hold and doesn't have a price target on the stock.

The National Highway Traffic Safety Administration, the agency responsible for road safety in the U.S., is looking at the videos.

"NHTSA is aware of the referenced [robotaxi] incidents and is in contact with the manufacturer to gather additional information," said the agency in an emailed statement. "NHTSA does not pre-approve new technologies or vehicle systems--rather, manufacturers certify that each vehicle meets NHTSA's rigorous safety standards, and the agency investigates incidents involving potential safety defects."

NHTSA has an open investigation of Tesla's driver assistance features. It isn't the first.

Investigations precede recalls, which require manufacturers to fix any issues identified. Tesla's driver-assistance software has been recalled in the past. Tesla fixed the issue via an over-the-air software update.

Investors will have to get used to evaluating robotaxi safety. Alphabet's Waymo completes more than 250,000 self-driving taxi rides a week. It reports a roughly 80% reduction in "injury-causing crashes." That is 223 fewer events, according to the company. That level of safety has been sufficient to keep Waymo operating smoothly and serves as a benchmark for investors to consider when tracking Tesla's data.

Exactly how good self-driving cars need to be is still up for debate. For now, "there's no question that [the Tesla launch] put a run up on the scoreboard, to use the baseball analogy," said Battle Road Research analyst Ben Rose, adding it's "the first inning."

Waymo has a few runs on the board, he said. Rose estimated that Waymo's annual revenue is approaching $260 million from completing 250,000 rides per week. He doesn't expect that makes Alphabet's self-driving taxi service profitable yet. A robo-taxi business will need more scale than that, with more taxis driving more riders.

Rose rates Tesla stock Buy and doesn't have a price target on the shares. A Buy rating for him means he expects Tesla stock to beat the market over the coming 12 months.

Looking ahead, there are questions about scaling at Tesla and Waymo, along with regulatory oversight and safety questions. Self-driving taxis are just getting started. Still, Tesla has that run on the board.