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Math Help - f ''(x)

  1. #1
    Junior Member
    Joined
    Aug 2009
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    31

    Unhappy f ''(x)

    I am very unsure of how to do this question..

    Suppose f ''(x) < 0 for all x, and suppose f(1)< f(3)< f(2). Prove that f(0)< f(2) and f(4)< f(2).

    Can somebody help me please?
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  2. #2
    Junior Member
    Joined
    Sep 2009
    Posts
    30
    Well if the second derivative is always negative, the original function must be always concave, like an 'upside down' quadratic. Draw one of these and think what it could mean if the y-value at x=2 is higher than that at both x=1 and x=3. Try plotting roughly where these points would lie on the quadratic and then plot f(0) and f(4) relative to the ones you've already marked. Look at the heights of these points relative to the other ones.
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