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Maxima/Minima Question

  1. Oct 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Find relative extrema of f(x).

    f(x) = [tex]\int^{x}_{0}[/tex] (t[tex]^{2}[/tex] -4)/(1 + cos(t)[tex]^{2}[/tex])


    2. Relevant equations
    N/A


    3. The attempt at a solution
    Is this correct?

    f '(x) = [(x² - 4)/(1 + cos²x)]

    Now set f '(x) = 0,
    [(x² - 4)/(1 + cos²x)] = 0
    x² - 4 = 0
    x = ± 2

    f'(x) is changing from negative to positive for both +2 and -2, so are both of them minima?
    (And would you have to take the derivative of the so-called f'(x) to get the actual derivative from which to calculate the max/min?)
     
    Last edited: Oct 17, 2009
  2. jcsd
  3. Oct 17, 2009 #2

    ideasrule

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    Your work is right; deriving an integral yields the original equation inside the integral.
     
  4. Oct 17, 2009 #3
    Thank you for the clarification. =)
     
  5. Oct 17, 2009 #4

    jbunniii

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    Gold Member

    No, that's not true. [itex]f'(x)[/itex] is an even function of [itex]x[/itex], so whatever its slope is at -2 must be the negative of its slope at 2.
     
  6. Oct 18, 2009 #5
    Ah; makes sense. Thank you for pointing this out!
     
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