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Mean value theorem problem

  1. Sep 19, 2013 #1
    1. The problem statement, all variables and given/known data
    Suppose that f(0)=-3 and f'(x)<=5 for all values of x. The the largest value of f(2) is
    A)7
    B)-7
    C)13
    D)8


    2. Relevant equations



    3. The attempt at a solution
    The problem can be easily solved using the mean value theorem but solving it in a different way doesn't give the right answer and I am not sure if the following is a valid approach.
    I have ##f'(x) \leq 5 \Rightarrow f(x) \leq 5x+c##, where c is some constant. At x=0, ##f(0) \leq c \Rightarrow c\geq -3##.
    At x=2, ##f(2)\leq 10+c##. The problem is that c can take any value greater than -3 and due to this I reach no answer. What is wrong with this method?

    Any help is appreciated. Thanks!
     
  2. jcsd
  3. Sep 19, 2013 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    f ' (x) = k ≤ 5. Integrating, f=kx+c and f(0)=-3. Therefore C=-3, well determined.

    ehild
     
  4. Sep 19, 2013 #3
    Really silly on my part, thank you very much ehild! :)
     
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