Marissa Mayer is in the fight of her life

Marissa Mayer in 90 seconds
Marissa Mayer in 90 seconds

Marissa Mayer is in the fight of her life, trying to overcome a growing chorus of calls for her dismissal from Yahoo.

Under intense criticism from shareholders, Mayer agreed to a PBS interview with Charlie Rose on Thursday.

Mayer was on the defensive, facing questions about what has gone wrong at Yahoo (YHOO) and whether she should be fired.

Rose: Do you think you'll be running Yahoo a year from now? I ask that because people ask that.

Mayer: I would love to be running Yahoo.... I would certainly hope that our services are here a year from now and that they run even better than they do today. And I can see it -- that should easily be the outcome. And we have a terrific team at Yahoo and I really hope that they're allowed to continue on to do the good work.

marissa mayer charlie rose
Mayer went on PBS' "Charlie Rose" Thursday.

Rose: Why is there so much criticism of Yahoo? They look at what you have done since 2012, and they say, she came in, and there was a flurry of acquisitions, including Tumblr. And most of them didn't work.

Mayer: I actually think they did work. I think that it really was a matter of, we needed to rebuild some of the talent base. We had, at the time, 50 engineers in a company of 14,000 working on mobile. Today we have more than 500 engineers working on mobile. We are one of the biggest app development shops in the world. I'm really proud of that. But we had to build that somehow. We built that through talent acquisitions. And so we saw the benefits of those acquisitions in the form of our mobile.

Rose: When you look at what has happened, what did you do wrong?

Mayer: I don't think the story has yet played out. And I think that when we look at this, we've rolled out a new strategic plan for the company, and we can see the turnaround. A lot of tech turnaround adds we do take five, six, seven years.

Fighting off the barbarians at the gate

The interview follows Yahoo's naming of two board members earlier on Thursday.

The new board members replaced two directors who resigned earlier this year, but the timing of the appointments is notable. Yahoo's board met with activist investors from hedge fund Starboard Value just after naming the new directors, according to the Wall Street Journal.

Yahoo is working to stave off a nasty battle with Starboard, which has threatened to nominate an alternate slate of directors for the company's board if Yahoo doesn't do more to boost its stock price.

The hedge fund has said that Mayer and her team have made no progress over the past three and a half years in their attempt to turn around Yahoo's fortunes. In January, Starboard managing member Jeff Smith called for "significant changes across all aspects of the business starting at the board level, and including executive leadership."

In response, Yahoo laid off 15% of its workforce last month as part of a plan to return the company to "modest to accelerating growth" next year and in 2018.

The new plan will focus on its core products and media brands in an attempt to save $400 million.

Related: Will Marissa Mayer be Yahoo's last CEO?

There's no guarantee that Mayer's new plan will succeed. Yahoo has already tried mass layoffs, reducing its staff by about a quarter since 2012, just before Mayer took over. The company has also done plenty of streamlining, killing off 121 products over the past three years.

A sale is one potential road out. Verizon (VZ) has publicly stated that it would consider buying Yahoo, and private-equity firm TPG Capital is rumored to have expressed interest.

Mayer is battling for her job on multiple fronts: the public, customers, investors and potential buyers.

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