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Rolle's/MVT Problem Need some help

  1. Dec 12, 2009 #1
    1. The problem statement, all variables and given/known data
    Does the function f exist when f(0)=-1, f(2)=4, and f'(x)≤2 for all values of x? Justify your answer.

    3. The attempt at a solution
    I am having some trouble with where to start...and end. Thanks for your help.
     
  2. jcsd
  3. Dec 12, 2009 #2

    Dick

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    What would the mean value theorem tell you about f(x) on the interval [0,2]?
     
  4. Dec 12, 2009 #3
    What would the mean value theorem tell you about f(x) on the interval [0,2]?
    It tells me that there exists a number c in (0,2) such that f'(c) = (f(2)-f(0))/(2-0)
     
  5. Dec 12, 2009 #4

    Dick

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    Ok. What is (f(2)-f(0))/(2-0) as a number?
     
  6. Dec 12, 2009 #5
    so 2.5 is not less than or equal to 2, so the function would not exist?
     
  7. Dec 12, 2009 #6

    Dick

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    Exactly.
     
  8. Dec 12, 2009 #7
    Great. Thank you, Sir.
     
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