Can Hewlett-Packard convince investors that it can keep growing in a weakening economy? That’s the key question facing the Palo Alto-based tech bellwether as it gears up to report first quarter earnings Feb. 19.

Although analysts don’t expect any surprises in the results from HP’s (HPQ) most recent quarter, they’re prepared to be surprised — in a bad way — by its guidance for the next. Like Apple (AAPL) and Cisco Systems (CSCO), companies that projected slower-than-expected revenue growth in the coming months (and whose shares took a hit as a result), the giant printer and PC maker could face tough times if consumer and corporate spending continues to slump.

“Their biggest challenge is the economy — just like every other company out there,” says American Technology Research analyst Shaw Wu. “This is a tough environment to be selling stuff in.”

Last week Wu lowered his target price for HP to $51 (the stock closed Thursday at $43.26), though he also added that the company is in a better position than most to “weather the storm.” It has “arguably the IT industry’s broadest portfolio of products,” he said. It sells to both the consumer and corporate markets and has a broad international footprint.

Selling hardware — printers, ink cartridges, computers — has long been HP’s bread and butter. Recently, though, it has started making a bigger push into software and services, such as its Snapfish online printing service.

About two-thirds of HP’s revenue come from outside of the United States — some of it from regions that have been largely untouched by the credit crisis. That’s an advantage analysts expect the CEO Mark Hurd to stress next week when he faces investors.

“HP generates over 65% of its revenues internationally, which should limit downside in case of a U.S. slowdown,” wrote Bernstein Research’s Toni Sacconaghi in a report to clients earlier this week.

According to Thomson First Call, analysts expect HP’s first quarter revenue to come in at $27.6 billion, with earnings per share of 81 cents.