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Using info from g' and g'' to find answer

  1. Apr 16, 2013 #1
    1. The problem statement, all variables and given/known data
    Let g be a twice differentiable function with g'(x)>0 and g''(x)>0 for all x.
    g(4)=12 and g(5)=18. Which is a possible value for g(6)?

    a)15
    b)18
    c)21
    d)24
    e)27

    2. Relevant equations
    slope=change y/ change x


    3. The attempt at a solution
    Ok so [g(5)-g(4)]/1=6
    a-c is eliminated since they produce slopes less than 6. Since we know g''(x)>0. the slope must be increasing.

    if g(6)=24 we get [g(6)-g(5)]/1=6. but this is a problem since the slope must be have increased from 4 to 5. So the answer is e) 27.

    Is my reasoning correct?
     
  2. jcsd
  3. Apr 16, 2013 #2

    jedishrfu

    Staff: Mentor

    Yes, you got it.

    As an analogy you could look at y=x^3, y'=3x^2 and y''=6x.
     
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