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Twice-differentiable Function and Etc.

  1. Apr 2, 2010 #1
    1. Let g be a twice-differentiable function with g'(x)>0 and g"(x)>0 for all real numbers of x, such that g(4)=12 and g(5) = 18. Of the following, which is the possible value for g(6)?

    2.I honestly have no idea where to start :-(
  2. jcsd
  3. Apr 2, 2010 #2


    Staff: Mentor

    g' > 0 for all x, so what does that tell you about the slope of g?

    g'' > 0 for all x, so what does that tell you about the concavity of g?

    I take it that this is a multiple choice problem, but you didn't include the possible answers in your problem description.
  4. Apr 2, 2010 #3
    If g'>0 and g">0 is the slope increasing and the concavity is upward? The choices are 15,18,21,24,27.
  5. Apr 2, 2010 #4


    Staff: Mentor

    Yes to both.
    You know that g(4) = 12 and g(5) = 18. If the function happened to be a straight line, its slope would be (18 -12)/(5 -4) = 6, so in that case, g(6) would be 24.

    The graph of g is not a straight line, since g'' > 0. This information eliminates all but one of the possible choices.
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