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Change in concavity of a function

  1. Mar 13, 2008 #1
    If n is a positive integer, how many times does the function f(x) = x^2 + 5cosx change concavity in the interval 0 <= x <= 2*pi*n?

    A) 0
    B) 1
    C) 2
    D) n
    E) 2n
  2. jcsd
  3. Mar 13, 2008 #2
    What do you think????

    And welcome to PF.
  4. Mar 13, 2008 #3
    I think its E.
  5. Mar 13, 2008 #4
    Why is that so?
  6. Mar 13, 2008 #5
    hint: find all points at which that function is concave up and concave down and see if you can determine how many times it changes it's concavity.
  7. Mar 13, 2008 #6
    The function changes concavity at an inflection point so we take the second derivative.

    f''(x) = 2-5cosx

    0 = 2-5cosx

    So whenever cosx = 2/5 there is a change in inflection. Then just figure out how many times that happens on [0,2pi*n]
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