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Math Help - horizontal tangent

  1. #1
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    horizontal tangent

    For what values of x does the graph of f (x) have a horizontal tangent? (Round the answers to three decimal places.) f (x) = 4 x 3 + 9 x 2 + 4 x + 1
    x1 = (smaller x-value)
    x2 = (larger x-value)



    how would i go about doing this problem
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  2. #2
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    Quote Originally Posted by kyleu03 View Post
    For what values of x does the graph of f (x) have a horizontal tangent? (Round the answers to three decimal places.) f (x) = 4 x 3 + 9 x 2 + 4 x + 1
    x1 = (smaller x-value)
    x2 = (larger x-value)



    how would i go about doing this problem
    Solve f'(x) = 0.
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  3. #3
    Super Member Bacterius's Avatar
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    A horizontal tangent means that the slope of the tangent is 0, right ? So you would basically get the derivative of your function and go hunting for solutions of f'(x) = 0.

    Your function is : f(x) = 4x^3 + 9x^2 + 4x + 1 (I assume, since it isn't clear in your message)

    Therefore, your derivative would be (don't click if you want to find by yourself) :

    Spoiler:
    f'(x) = 12x^2 + 18x + 4


    Therefore, you would be solving f'(x) = 0, which is easy since f'(x) is a quadratic equation. All right ?
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