1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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)?


    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


    Staff: Mentor

    Yes, you got it.

    As an analogy you could look at y=x^3, y'=3x^2 and y''=6x.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted