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Mean Value Theorem

  1. May 5, 2013 #1
    1. The problem statement, all variables and given/known data

    State the Mean Value Theorem and find a point which satisfies the conclusions of the Mean Value Theorem for f(x)=(x-1)3 on the interval [1,4].

    2. The attempt at a solution

    Mean Value Theorem:states that there exists a c∈(a,b) such that f'(c)=[itex]\frac{f(b)-f(a)}{b-a}[/itex]

    3(x-1)2=[itex]\frac{27-0}{4-1}[/itex]

    3(x-1)2=[itex]\frac{27}{3}[/itex]

    3(x-1)2=9

    →(x-1)2=3

    →x=1±√3

    ∴x=1+√3 which lies on the interval [1,4].

    I was wondering if I did the question correctly and if there was anything further I should add.
     
    Last edited: May 5, 2013
  2. jcsd
  3. May 5, 2013 #2
    This is all good. Almost. You need to state certain conditions for f(x) and verify that the given f(x) meets them.
     
  4. May 5, 2013 #3
    What 'certain condition' are we talking about here?
     
  5. May 5, 2013 #4
    The hypothesis of the MVT; that f is continuous on the interval and differentiable every in the interior of the interval.
     
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