Question 789294
This is sometimes true.  <P>
The Intermediate Value Theorem states that if f is continuous on a closed interval [a,b], f(a) does not equal f(b), and k is any number between f(a) and f(b), then there is at least one number c in [a,b] such that f(c)=k.<P>
In this case f(c) =k is not between f(2) and f(11).  For a sin function, for example, this could be true.  For a straight line function, it is false.  So it's sometimes true.<P>
Note the problem may not be written correctly.  It indicates that f is continuous at the end points.  It does not specify that the function is continuous in the interval [a,b].  If that's intentional, then the answer is still sometimes true.