Age can be a sensitive topic for anyone — especially world-class athletes.

Take, for example, Elvis Dumervil.

On Tuesday, the 49ers’ newly signed pass rusher met Bay Area reporters for the first time, and he stopped a reporter in mid-question after his “age” was invoked.

“My age?” Dumervil said. “What about my age?”

Dumervil is 33. And the reporter noted that’s old for an NFL player.

“Is it?” Dumervil said, smiling during the good-natured back-and-forth. “I learned something now.”

Plenty of 49ers can learn something from Dumervil, a 12-year veteran who is the second-oldest player on the team behind placekicker Robbie Gould, 35. However, the 49ers hope Dumervil isn’t merely a mentor; they signed him last week because they believe the five-time Pro Bowl selection can still menace quarterbacks.

Not surprisingly, Dumervil, who ranks seventh among active players in sacks (99), thinks he’s ready to showcase his 2014 form (17 sacks) after an Achilles injury partly explains his relatively paltry production over the past two seasons with the Ravens (nine sacks in 24 games).

What’s his message for those who think his best days are behind him? Dumervil answered by noting he’s accustomed to sacking his skeptics: He was a fourth-round pick by the Broncos out of Louisville partly because he’s 5-foot-10.

“In my career, I’ve always had those types of challenges and obstacles,” Dumervil said. “That’s the beauty about it. In the NFL, there’s opportunity day in and day out, week in and week out, to prove yourself. It’s a young man’s game. And I’m excited to play a young man’s game.”

The 49ers are betting the old guy (sorry, Elvis) can still compete with kids based on his finishing kick in 2016.

Dumervil underwent surgery in February 2016 to repair an Achilles tendon that was 60 percent torn. The injury had become progressively worse during the 2015 season, when he played all 16 games and recorded six sacks despite dealing with pain starting in training camp. Last year, Dumervil missed eight of the first 10 games before registering his three sacks in the final six contests.

The 49ers, who didn’t draft an outside pass rusher until the sixth round, were impressed after studying the finish to Dumervil’s season.

“I think he put it on tape at the end of last year when he started to get more over his injury,” head coach Kyle Shanahan said. “… I think Elvis lives and dies getting to the quarterback. He’s thinking about it all the time, every day: when he’s in the building and when he’s outside the building.”

Dumervil could share snaps with Arik Armstead at the “Leo” defensive end position, which is reserved for the team’s most ferocious pass rusher.

Armstead, 23, hopes to prove he can generate outside pressure after mostly playing inside during his first two seasons. And Dumervil hopes to prove he can still do what he’s done for most his decorated NFL career.

“Everyone has an opinion, and you have to respect that,” Dumervil said of his doubters. “The beautiful thing about life is you can wake up every day and prove otherwise.”

Briefly: The 49ers’ eight coaching fellows who will be with the team through training camp include Katie Sowers, who is the first woman to coach with the 49ers. Sowers interned with the Falcons last year. … Rookie quarterback C.J. Beathard signed a four-year contract, making defensive lineman Solomon Thomas of Stanford the only one of the 49ers’ 10 draft picks who remains unsigned. … Thomas can join the 49ers for the final day of their mandatory minicamp Thursday, although the last day won’t include a practice. Due to an NFL rule, Thomas has been unable to participate in the offseason program since he attended rookie minicamp because he went to a school which uses the quarter system. Stanford will have final exams Wednesday.

Eric Branch is a San Francisco Chronicle staff writer. Email: Twitter: @Eric_Branch

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