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Satisfying the Mean Value Theorem

  1. Nov 5, 2011 #1
    1. The problem statement, all variables and given/known data
    For what values of a,m, and b does the function

    satisfy the hypothesis of the Mean Value Theorem of the interval [0,2].

    2. Relevant equations
    (f(b) - f(a))/(b-a) = f'(c)

    3. The attempt at a solution
    So, I wanted to make a point of continuity for the whole equation. So, I set the equation to x=1 in both cases and then equated them, and got;
    2+a=m+b ---> a=m+b-2

    Then, I found the derivative of the original equation and set x again to 1, then equated the two given that were diffable, and got;

    Now I can't get any values for a,b, or m without getting:

    I must be doing something wrong.
  2. jcsd
  3. Nov 5, 2011 #2


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    The derivative of mx + b is not m + b and the derivative of -x2+3x + a is not -2x+3+a. Also don't forget you will need continuity at x = 0.
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