SAN FRANCISCO (AP) — Apple has spent most of this year promising to defy the skeptics who believe the iPhone and iPad maker lost its ingenuity when Steve Jobs died in 2011.

This week should provide a better sense of whether Apple is heading down promising new avenues of growth or whether it's still wandering aimlessly around well-trod territory in search of another breakthrough.

If speculation pans out, Apple could use its annual developers conference in San Francisco as a showcase for its plans to help manage people's health, finances and homes. The five-day conference begins Monday.

Apple Inc. CEO Tim Cook declined to provide specifics about the agenda during an interview with The Associated Press last week about the company's $3 billion deal for headphone and music-streaming specialist Beats Electronics.

"We have some great things coming out this year, and I think people are going to be blown away," Cook said. "I am certainly blown away from playing with them."

Investors appear to be regaining faith in Apple's ability to innovate. The company's stock has climbed 13 percent so far this year to close Friday at $633. The Standard & Poor's 500 index has gained 4 percent during the same stretch.

The rally reflects a dramatic turnaround in sentiment. Apple financial growth has slowed amid tougher competition, and it has had a streak of ho-hum product updates. As a result, Apple's stock fell 45 percent to $385.10 in April 2013, from a peak of $705.07 in September 2012.

Some of the recent run-up may have been triggered by a planned 7-for-1 stock split that will make Apple's stock cheaper to buy. The ability for more investors to afford the stock and participate in the market could drive up the company's overall market value. The split, announced in April, is planned for June 9.

Monday's keynote is expected to focus on the software that runs Apple's mobile devices and Mac computers. Apple typically rolls out its latest gadgets at separate gatherings timed to the holiday shopping season. The developers conference is where the Cupertino, California, company provides the first glimpse of software updates coming to those gadgets.

Even without a new iPhone, iPad or even a long-rumored smartwatch likely to be unveiled this week, Apple could still draw interest by revealing its plans to immerse its services even deeper in people's lives.

The next version of Apple's mobile software, iOS, is widely expected to include a built-in health-management tool to help people track their vital signs, diet and sleeping habits. This tool could be similar to Passbook, a feature that Apple built into iOS two years ago to store tickets for flights and events, as well as digital gift certificates.

The new iOS also could include a long-awaited digital wallet that enables Apple to process payments on iPhones and iPads. Google Inc. has already tried something similar on its Android software for smartphones, but it hasn't gained much traction in digital payments.

Apple, though, already has built a powerful springboard into digital payments — 800 million iTunes accounts tied to credit cards. The iPhone also includes a location technology, called iBeacon, that conceivably could be tied into a digital wallet. Apple already has been working with various merchants to use iBeacon so they might be able to communicate with shoppers as they roam through the store. Mobile payments are believed to be high on the priority list of Angela Ahrendts, the former Burberry CEO who became the head of Apple's own stores in April.

Other speculation has centered on the possibility that Apple will unveil a home automation system that will enable iPhones and iPad to become a remote control for managing lighting, security and other household appliances with wireless connections.