On Friday morning, shares shot up more than 3% before falling back to $36.26, a 1% increase, following news that CEO Dick Costolo was stepping down.
Twitter shares had fallen more than 25% in the last three months as Costolo struggled to boost growth and profits and deal with management dysfunction.
Despite the shortcomings of the company's strategy, the company's incoming interim CEO Jack Dorsey said he would not be changing its direction, describing the "fundamentals" the company is building right now as "extremely strong and beautiful."
When asked whether a potential takeover of the company was on the table, both Dorsey and Costolo told CNBC they believe they can "maximize value" best as an independent company, but they didn't rule out a takeover entirely, saying they were going to fulfill their fiduciary duty to shareholders. Costolo declined to comment further on takeover speculation.
Some analysts said it may be too early to consider a potential takeover.
Regardless of whether a takeover is on the table, analysts agree Twitter has a slew of problems it needs to quickly address. Growth has stagnated for the microblogging service and advertising never became as lucrative as investors wanted.
And there is also a user experience problem: Outside of the media and entertainment worlds, the site continues to baffle many people who aren't familiar with its 140-character limits, hashtags, lists and retweets.
Simply put, many still don't understand what Twitter is for.
Perhaps with that in mind, Twitter said Thursday that it would remove the 140-character limit on private messages between two users, known as direct messages.
Public posts, or tweets, would still carry the limit.
The San Francisco company will now look both internally and externally for a replacement for Costolo. Costolo's departure becomes effective July 1. At that time, co-founder Jack Dorsey will take the helm as interim CEO.
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