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Homework Help: Mean Value Theorem Help

  1. Dec 12, 2009 #1
    1. The problem statement, all variables and given/known data
    Let us suppose that, 3≤ f '(x) ≤5 for all x values. Show that 18≤ f(8) - f(2) ≤30.

    3. The attempt at a solution
    Alright folks... I am unsure where to start, or where to apply the MVT or the Rolle's Theorem.

  2. jcsd
  3. Dec 12, 2009 #2
    Well the mean-value theorem states that you can find some c in the interval (2,8) such that:
    [tex]f'(c) = \frac{f(8)-f(2)}{8-2}[/tex]
    Now just note:
    [tex]3 \leq f'(c)=\frac{f(8)-f(2)}{8-2} \leq 5[/tex]
  4. Dec 12, 2009 #3
    Alright, I understand that that is the equation of the secant line. How do I prove that it is ≤18 and ≤30?
  5. Dec 12, 2009 #4
    You have:
    [tex]3 \leq \frac{f(8)-f(2)}{6}\leq 5[/tex]
    by my previous post. Multiplying by 6 you get:
    [tex]3\times 6 \leq f(8)-f(2)\leq 5\times 6[/tex]
  6. Dec 12, 2009 #5
    Oh... silly me. You multiply the six out of the bottom.
    Thanks man, that really helped. Much love brah.
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