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: Inflection Points question

  1. Nov 12, 2009 #1
    1. The problem statement, all variables and given/known data
    f(x)=-8x4-5x3 +3 for concavity and inflection points.

    2. Relevant equations
    f(x)=-8x4-5x3 +3

    3. The attempt at a solution
    can someone explain to me what exactly Inflection Points are?
    is it like critical points for the first derivative but those are for the second one?
    i mean, making f''(x) = 0 and get 2 numbers and those are the Inflection Points?
  2. jcsd
  3. Nov 12, 2009 #2
    Indeed. Inflection points are where the function changes from being concave-up to concave-down or vice versa. This is the same as the local extrema of the derivative, or the roots of the second derivative.
  4. Nov 12, 2009 #3
    so i would do this

    x=0, 10/32

    and those are my answers? well i tried and it doesnt work.. :(
  5. Nov 12, 2009 #4


    Staff: Mentor

    f''(x) = -96x2 - 30x = -6x(16x + 5)
    So f''(x) = 0 for x = 0 and x = -5/16
  6. Nov 12, 2009 #5


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    No, it isn't quite the same. The roots of the second derivative are the values of x where there may but there need not be an inflection point. You must always additionally check that the second derivative actually changes sign at those roots. For example, if

    [tex]f''(x) = (x-2)(x-5)^2[/tex]

    then x = 2 gives location for an inflection point but x = 5 does not.
  7. Nov 12, 2009 #6
    oh yeah i didnt notice the - sign mistake :S

    there is a second part to this question which asks to find the points where it concaves up and down.
    the graph of f is only concaving up isnt it?
  8. Nov 12, 2009 #7


    Staff: Mentor

    The graph of f is concave up (concaving isn't a word) when f''(x) > 0, and is concave down when f''(x) < 0. For your problem, f''(x) is positive for some x values and negative for other x values.
  9. Nov 12, 2009 #8
    this is how the question is constructed:
    "f is concave down on (-infty ,___)U(___, infty) and its concave up on (___,___)"

    since f''(x) = 0 for x = 0 and x = -5/16
    so when you said "f''(x) is positive for some x values and negative for other x values"
    ==> x = 0, -5/16

    so would it be:
    "f is concave down on (-infty ,-5/16)U(0, infty) and its concave up on (-5/16,0)"
  10. Nov 12, 2009 #9


    Staff: Mentor

    Works for me.
  11. Nov 12, 2009 #10
    sweet... thanks for your explanation!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook