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: Definitely Maybe: Concavity and Point of Inflection

  1. Dec 2, 2009 #1
    1. The problem statement, all variables and given/known data
    f is a continuous function on [0, 8] and satisfies the following:
    Second Derivative Sign Test
    x ; f''
    0 [tex]\leq[/tex] x < 3 ; -
    3 ; 0
    3 < x < 5 ; +
    5 ; Does Not Exist
    5 < x < 6 ; -
    6 ; 0
    6 < x [tex]\leq[/tex] 8 ; -

    Based on this information is there a point of inflection at x = 5?
    (a) Definitely
    (b) Possibly
    (c) Definitely not

    2. Relevant equations
    Definition: A point of inflection is where the concavity changes and there is a tangent line.

    Concavity changes when f'' changes signs. Negative f'' means concave down; positive f'' means concave up.

    3. The attempt at a solution
    There is a sign change at f''(5), but the correct answer could either be "definitely" or "possibly." The point of inflection does not exist, but there is still a sign change, meaning it is a point of inflection. But my class and I were wondering whether it was possible that because there is no derivative at x = 5, there could also possibly be or not be a point of inflection there, too. The book says it's "possibly" a point of inflection, but going by the definition, we just presumed it to "definitely" be one.
  2. jcsd
  3. Dec 3, 2009 #2
    Can you think how this would reflect on the question? Can you think of two examples to satisfy the conditions on f''(x), one that does not have a tangent at x=5 and one which does?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook