anonymous
  • anonymous
Let f(x) = (x − 3)−2. Find all values of c in (1, 4) such that f(4) − f(1) = f'(c)(4 − 1).
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
a bit confusing does it really say \[f(x)=(x-3)-2\]?
anonymous
  • anonymous
because that is just \(x-5\)
whpalmer4
  • whpalmer4
I'm guessing it is \(f(x) = (x-3)^{-2}\)

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anonymous
  • anonymous
it is raised to the -2
whpalmer4
  • whpalmer4
@alexthomas so how about putting in a ^ so we know that? pretend we can't actually see your book or paper or screen :-)
anonymous
  • anonymous
my bad...sorry for not being clear
whpalmer4
  • whpalmer4
not the first it has happened on openstudy, certainly won't be the last time, but you can try to make it the last time you do it :-)
anonymous
  • anonymous
did you find the derivative?
anonymous
  • anonymous
i belive the derivative is |dw:1371518374836:dw|
anonymous
  • anonymous
it is "does not exist" thank you anyways
anonymous
  • anonymous
yeah the point you are looking for may or may not exist the function \[f(x)=\frac{1}{(x-3)^2}\] is not continuous on the interval \((1,4)\)
anonymous
  • anonymous
therefore it does not satisfy the hypothesis of the mean value theorem that doesn't mean the number doesn't exist, it just means it is not guaranteed to exist
anonymous
  • anonymous
thank you
anonymous
  • anonymous
yw

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