Is this the right course for this kind of questions

[transgalactic]

i found this calculus course:

http://ocw.mit.edu/OcwWeb/Mathematics/18-01Fall-2006/VideoLectures/index.htm

does it consists with theoretical knowledge of solving question like this:

there is a function f(x) which is continues in the borders [a,b]
and derivitable in the borders (a,b), b>a>0
alpha differs 0
prove the there is b>c>a

in that formula:
http://img392.imageshack.us/my.php?image=81208753je3.gif

i never encoutered this kind of questions
and in this MIT calculus course i searched their exams and there is no such question
there are only normal calculus material regarding derivatives ,limits,aproximations
but i can't see this sort of complicated proving questions
??

 

[transgalactic]

what additional text besides normal calculus should i read in order to
solve this question