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Is this the right course for this kind of questions

  1. Nov 15, 2008 #1

    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:

    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 cant see this sort of complicated proving questions
  2. jcsd
  3. Nov 15, 2008 #2


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    [tex]\frac{left|\begin{array}{cc}a^\alpha & b^\alpha \\ f(a) & f(b) \end{array}\right|}{a^\alpha- b^\alpha}= f(c)- c\frac{f'(c)}{\alpha}[/tex]

    [tex]\frac{a^\alpha f(b)- b^\alpha f(a)}{a^\alpha- b^\alpha}= \frac{a^\alpha f(b)- a^\alpha f(a)+ a^\alpha f(a)- b^\alpha f(a)}{a^\alpha- b^\alpha}[/tex]
    [tex]\frac{a^\alpha}{a^\alpha- b^\alpha}(f(b)- f(a))+ f(a)[/tex]

    That looks to me like a fairly straight forward variation of the "mean value theorem". I would have no doubt that any Calculus course would include a proof of the mean value theorem but I certainly would not guarentee any course would include that particular variation.
  4. Nov 15, 2008 #3
    so these proof questions are about theorems

    how much theorems are there in a single variable calculus course
    where can i effectively learn them,understand them ?
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