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Math Help - equation of tangent, normal line and vertex?

  1. #1
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    equation of tangent, normal line and vertex?

    for the function f(x) = 2x^2 - 8x - 5
    how do i find equation of tangent, and equation of normal line to the curve y = f(x) at (1, f(1)) ? and vertex?

    as far as i know, for the normal line,
    f(#), so it would be (1,f(#))
    and - 1/f'(x) is normal line
    but i don't know how to find "equation" of normal line, and equation of tangent. and vertex........?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Recall the point slope form of a line through(x0,y0)

    y = m(x-x0) + y0

    For the tangent line m = f '(x0) for the normal line m =-1/f ' (x0)

    For the vertex don't forget your college algebra --complete the square!!
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  3. #3
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    so from here, y = m(x-x0) + y0, is m = f'(x) ?
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  4. #4
    MHF Contributor Calculus26's Avatar
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    m = f ' (1) since you want the tangent line at x = 1

    Note if you use f ' (x) you don't even get a linear equation
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  5. #5
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    Quote Originally Posted by Calculus26 View Post
    Recall the point slope form of a line through(x0,y0)

    y = m(x-x0) + y0

    For the tangent line m = f '(x0) for the normal line m =-1/f ' (x0)

    For the vertex don't forget your college algebra --complete the square!!
    thank you for your helping,Calculus26.
    i found equation of tangent and normal line, however, i still have no clue how to find vertex using calculous..
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  6. #6
    MHF Contributor Calculus26's Avatar
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    Hint the vertex is the minimum---What is f ' at a minimum ?
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  7. #7
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    Complete the square to answer Caculus26's question.
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  8. #8
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    Quote Originally Posted by Calculus26 View Post
    Hint the vertex is the minimum---What is f ' at a minimum ?
    i've tried this way (if this wasn't where you were trying to get me on)

    so im looking for the vertex... which will have horizontal line,
    i.e. f'(x) = 0

    f'(x) = 4x - 8 = 0
    x = 2

    v= (2, f(2))

    f(2) = 2(2^2)-8(2)-5
    = -13

    so vertex will be (2,-13)

    did i do it correctly?
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  9. #9
    MHF Contributor Calculus26's Avatar
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    you got it now
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