SOLUTION: Let f be continuous where f(2)=-4 and f(11)=9. Classify the statement as always, sometimes or never true. There exists c in (2,11) such that f(c)=20.

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.

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.

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.