PRESCOTT, Ariz. >> Even while being held hostage by Islamic State extremists, Kayla Mueller found good in everything.

She taught her guards how to do crafts and make peace birds out of paper. She stood on her head for exercise in her cramped quarters. And she wrote uplifting letters home despite being a prisoner of a brutal terrorist regime.

"I have come to see that there is good in every situation, sometimes we just have to look for it," she wrote.

The portrait of the 26-year-old humanitarian aid worker from Prescott, Arizona, came as her death was confirmed Tuesday by the U.S. government. Family members spoke fondly of her free spirit and efforts to ease the suffering of others as a small memorial of flowers and handwritten notes took shape near a sign calling on people to "Pray for Kayla."

It’s the same space where people in the city of about 40,000 gathered not too long ago to honor 19 Prescott-based members of an elite fire crew who died in 2013 in the deadliest single day for firefighters since Sept. 11, 2011.

Mueller was captured in August 2013, but her captivity had largely been kept secret in an effort to save her. President Barack Obama said a military operation last summer to recover Mueller and others failed when rescuers arrived only "a day or two" after the group had been moved.

Arizona Sen. John McCain and Rep. Paul Gosar, a Republican who represents Prescott, were in close contact with the family and government officials throughout the ordeal, with the senator traveling to Syria at one point to meet with members of the army fighting President Bashar Assad.

Gosar told The Arizona Republic that one effort to free Mueller involved a man who traveled to the Syrian prison camp where Mueller was being held. The man told the captors he was Mueller’s husband in a ruse designed to free her, Gosar said, but it didn’t work. In addition, Gosar’s office said the name of Aafia Siddiqui, a Pakistani scientist convicted of shooting at two U.S. soldiers in Afghanistan, came up in discussions with Islamic State over Mueller. Siddiqui is an American-educated woman whose release has long been sought by terrorists.

In her hometown, residents began to honor Mueller on Tuesday. Her family has encouraged people to donate to organizations Mueller would have supported, saying big displays of support wouldn’t mesh with her humble nature. Prescott Mayor Marlin Kuykendall said he would take cues from the family on any public memorials.

Mueller’s aunt, Lori Lyon said her niece has touched the hearts of people around the world who want to be more like the globe-trotting aid worker.

"And if that is her legacy and the footprint that she leaves on the world," Lyon added, dissolving into tears, "then that is a wonderful thing."

From Prescott, she helped raise awareness of HIV and AIDS and offered comfort at a women’s shelter. In Flagstaff, where she attended Northern Arizona University, she protested genocide in Darfur. Her desire to help others stretched beyond Arizona to Palestine, Israel, India, France and Syria.

"I’m not sure yet how to live in a world without Kayla, but I do know that we’re all living in a better world because of her," said a tearful Eryn Street, one of Mueller’s closest friends as she spoke from the courthouse plaza in Prescott on Tuesday.

The Islamic State group claimed Friday that Mueller had died in a recent Jordanian airstrike targeting the militants. The Pentagon said it doesn’t know how she died but is certain it was not during the airstrike.

President Barack Obama pledged to bring Mueller’s captors to justice "no matter how long it takes." The White House said Obama had spoken with Mueller’s parents and offered prayers. From Jordan, government spokesman Mohammed al-Momani offered his country’s condolences.

Mueller wrote passionately about conditions in war-torn Syria, where she had gone to help refugees. In a blog post, she wrote: "Every human should act. They should stop this violence."

Her family and friends told of simple things Mueller did, such as such as giving people food and water, and searching for clothing and housing. Street recalled the two of them making the best of their car breaking down about a half mile from Street’s home. Getting the car towed would be no fun, she said.

"Instead, we turned on Bob Marley on full blast on the radio and, with the car in neutral, we started pushing that golden brown chariot home," she said.

Prescott, the former territorial capital of Arizona, only recently begun to recover from the deaths of the firefighters. Stickers featuring the fire crew’s logo and bearing the number "19" are still fixed to vehicles all around town. The mountain town resembles a relic of the Old West in many ways, with its colorful downtown saloons.

"What a fine, fine woman and a tribute to Prescott," said resident Tina Nemeth. "It’s just so sad, it really is, and everyone feels exactly the same. It’s a shock it hit Prescott. We’re not that big of a town."

Mueller is the fourth American to die while being held by Islamic State militants. Three others — journalists James Foley and Steven Sotloff and aid worker Peter Kassig — were beheaded by the group.

Obama on Tuesday defended a policy in which the U.S. has refused to pay huge ransoms, saying in an interview with BuzzFeed News that doing so would only encourage more kidnappings. He said explaining the policy to victims’ families is "as tough as anything I do."