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Math Help - Derivatives Problem

  1. #1
    Member FalconPUNCH!'s Avatar
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    Derivatives Problem

    For what values of x does the graph of:

    F(X) = X^3 + 3X^2 + X + 3 have a horizontal tangent?

    I don't know how to approach this but I got 0 as one of the values of X. I'm not really sure if there are other values.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by FalconPUNCH! View Post
    For what values of x does the graph of:

    F(X) = X^3 + 3X^2 + X + 3 have a horizontal tangent?

    I don't know how to approach this but I got 0 as one of the values of X. I'm not really sure if there are other values.
    The slope of the tangent is the derivative, so
    F^{\prime}(X) = 3X^2 + 6X + 1

    You are looking for a horizontal tangent, so you are looking for a slope of 0. Thus you are looking for a value of X such that
    3X^2 + 6X + 1 = 0

    -Dan
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  3. #3
    Member FalconPUNCH!'s Avatar
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    Quote Originally Posted by topsquark View Post
    The slope of the tangent is the derivative, so
    F^{\prime}(X) = 3X^2 + 6X + 1

    You are looking for a horizontal tangent, so you are looking for a slope of 0. Thus you are looking for a value of X such that
    3X^2 + 6X + 1 = 0

    -Dan
    So do I have to use the quadratic formula in order to do it? If so then I did it earlier today
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by FalconPUNCH! View Post
    So do I have to use the quadratic formula in order to do it? If so then I did it earlier today
    yes, that is one way. there's no nice way to factor this as there are no rational roots
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  5. #5
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    If you have a graphing calculator like a TI-83 you can type in the equation for the derivative and then hit 2nd --> Calc to find the zeros. I'm guessing your teacher probably wants to see work and it doesn't hurt to practice by hand, but it's a good way to check your answers
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    Re:

    Quote Originally Posted by FalconPUNCH! View Post
    For what values of x does the graph of:

    F(X) = X^3 + 3X^2 + X + 3 have a horizontal tangent?

    I don't know how to approach this but I got 0 as one of the values of X. I'm not really sure if there are other values.
    RE:
    Attached Thumbnails Attached Thumbnails Derivatives Problem-79.gif  
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  7. #7
    Member FalconPUNCH!'s Avatar
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    Quote Originally Posted by Jhevon View Post
    yes, that is one way. there's no nice way to factor this as there are no rational roots
    I just did it with the quadratic formula. Thank you guys for helping
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