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Math Help - Local Maxima of a definite integral...

  1. #1
    Member dokrbb's Avatar
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    Local Maxima of a definite integral...

    I have such a question: - at what value of t does the local maxima of f(t) occur?

     f(t) = \displaystyle \int_{0}^{t} \left( \frac{x^2 +10x + 24}{1 + cos^2(x)} \right)dx

    so, my attempts in the base of the part 1 of the FTC I have

     f'(t) = \left( \frac{t^2 +10t + 24}{1 + cos^2(t)} \right)dx , since the denominator would never be  = 0 I evaluated the numerator

    which gave me two critical points  x_1 = -4; x_2 = -6, and evaluating the f''(t) at those points gave me (-4) > 0 , and local maxima, but it actually is considered wrong in my homework,

    what did I miss here?
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Local Maxima of a definite integral...

    Never mind. I was looking as derivative not overall function.

    -Dan

    It seems that I can't remove the attached image. Ah well.
    Attached Thumbnails Attached Thumbnails Local Maxima of a definite integral...-local.jpg  
    Last edited by topsquark; September 23rd 2013 at 06:38 PM. Reason: Looking as derivative not overall function.
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  3. #3
    Junior Member FelixFelicis28's Avatar
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    Re: Local Maxima of a definite integral...

    Quote Originally Posted by dokrbb View Post
    I have such a question: - at what value of t does the local maxima of f(t) occur?

     f(t) = \displaystyle \int_{0}^{t} \left( \frac{x^2 +10x + 24}{1 + cos^2(x)} \right)dx

    so, my attempts in the base of the part 1 of the FTC I have

     f'(t) = \left( \frac{t^2 +10t + 24}{1 + cos^2(t)} \right)dx , since the denominator would never be  = 0 I evaluated the numerator

    which gave me two critical points  x_1 = -4; x_2 = -6, and evaluating the f''(t) at those points gave me (-4) > 0 , and local maxima, but it actually is considered wrong in my homework,

    what did I miss here?
    Maxima are indicated by f''(t) < 0, OP.
    Last edited by FelixFelicis28; September 23rd 2013 at 06:48 PM.
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    Forum Admin topsquark's Avatar
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    Re: Local Maxima of a definite integral...

    This is not my day!

    -Dan
    Last edited by topsquark; September 23rd 2013 at 06:47 PM. Reason: (sighs) Not again!
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    Member dokrbb's Avatar
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    Re: Local Maxima of a definite integral...

    I got it guys, it is actually the another one  x = -6 at wich it gives f''(x) < 0 ... why I was looking for the >0 values...,

    thanks for your input,
    dokrbb
    Last edited by dokrbb; September 23rd 2013 at 07:40 PM.
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