What is the significance of company A's stock price on December 10th, 2005?

[Numnum]

Homework Statement

You know that the only time company A's stocks were traded for $25 a share was on December 10th, 2005. You also know that on June 3rd of 2001 the price was $41 a share and on September 17th of 2010 it was $34. Assuming that stock prices change continuously, what conclusion can you make about company A's stock price on any other day?

Homework Equations

The Attempt at a Solution

The stock doesn't seem to change much everyday. Maybe there's never a price spike?

 

[Mute]

You're told that the only time the company's stock price was at $25/share was December 10th, 2005. You are then given prices on two more days, one before Dec 10, 2005, and one after. Are those prices higher or lower than $25. If the prices change have to change continuously between those three dates, what does knowing that Dec 10, 2005 was the only day the price was $25 tell you?

 

[Numnum]

You're told that the only time the company's stock price was at $25/share was December 10th, 2005. You are then given prices on two more days, one before Dec 10, 2005, and one after. Are those prices higher or lower than $25. If the prices change have to change continuously between those three dates, what does knowing that Dec 10, 2005 was the only day the price was $25 tell you?

$25 was the minimum? And two days other than Dec 10 can have the same stock price?

 

[Mute]

$25 was the minimum? And two days other than Dec 10 can have the same stock price?

Yes - what kind of minimum is it (local/global)? (Assuming the price has yet to dip below $25 at some point in the future). It's certainly true that it's possible that prices of $34 and $41 can occur more than once. In fact, you know that it has to cross one of those prices at least twice - which one.

I'm not sure if the question wants you to draw any other conclusions, but those were the ones that occurred to me.