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Question about fundamental thm calc part 1

  1. Dec 3, 2011 #1
    If f is continuous on [a,b] then the fucntion g defined by
    g(x) = ∫f(t)dt a <= x <= b is continuous on [a,b] and differentiable on (a,b) and g' = f

    Question....

    If f is continuous on [a,b], then why is g only differentiable on (a,b)?
    This does not make sence... if g' = f g should be diff on [a,b] after making the first statement "f is continuous on [a,b]"
     
  2. jcsd
  3. Dec 3, 2011 #2
    The thing is that differentiability is often only defined on open intervals. This is likely what your text has done.

    If you want g to be differentiable on [a,b], then you need to have a definition for differentiability on closed intervals.

    Mod note: as this is not a homework problem, I mover it to the math forums.
     
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