1. Not finding help here? Sign up for a free 30min 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!

Inflection Points

  1. Feb 28, 2008 #1
    1. The problem statement, all variables and given/known data
    Explain how you can locate the local maxima and minima for the graph of y=f '(x) by examining the graph of y=f(x).

    2. Relevant equations



    3. The attempt at a solution
    In the back of the book the answer reads:
    If there is an inflection point on the graph of y=f(x) at x=c, then f(x) must change concavity at x=c. Consequently, f '(x) must change from increasing to decreasing or from decreasing to increasing at x=c, and x=c is a local extremum for f '(x). If there is an inflection point on the graph of y=f(x) at x=c, then f(x) must change concavity at x=c. Consequently, f '(x) must change from increasing to decreasing or from decreasing to increasing at x=c, and x=c is a local extremum for f '(x).


    I must be missing something. Don't you need to know the second derivative in order to know where the inflection points actually are?
     
  2. jcsd
  3. Feb 28, 2008 #2
    Maybe they're just asking you to locate, by actually plotting y=f(x), its inflection points.
     
  4. Feb 29, 2008 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Well, not by plotting a specific function, but just explaining that at an inflection point, the graph changes from "convex up" to "convex down". Typically we find the second derivative, in order to find the inflection points, in order to tell where the curve changes convexity. The point of this problem is we can do it, at least roughly, the other way. If we look at the graph and can see where it changes convexity, we can see where the inflection points are (and, so, where the second derivative is 0).
     
  5. Feb 29, 2008 #4
    oh

    ohh alright. thanks ivy.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Inflection Points
  1. Inflection points (Replies: 9)

  2. Inflection point (Replies: 1)

  3. Point of inflection (Replies: 6)

  4. Points of Inflection (Replies: 4)

  5. Point of inflection (Replies: 4)

Loading...