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Math Help - Tangent lines!!

  1. #1
    ohmygodshoes
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    Tangent lines!!

    alright...im trying to find the tangent line of

    f(x) = ln(x) at x = 4

    so i know that the slope simply equals f`(x) which is

    f`(x) = 1/x = 1/4 = m

    then i use that in the equation of a tangent line,

    y = mx + b

    then i use the values of x and y from f(x) = ln(x) and i get

    f(4) = ln(4) = .4 so x = 4 , y = 1.4

    then plugging these in the equation i get

    1.4 = 1/4(4) + b and then this equals b = 1.4 - 1 = .4 so b = .4

    now i plug all these values in and get

    y = 1/4x + .4

    but i got it wrong...can someone please tell me why and show me how i messed up...thanks
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  2. #2
    Super Member
    earboth's Avatar
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    Quote Originally Posted by ohmygodshoes View Post
    alright...im trying to find the tangent line of

    f(x) = ln(x) at x = 4

    so i know that the slope simply equals f`(x) which is

    f`(x) = 1/x = 1/4 = m

    then i use that in the equation of a tangent line,

    y = mx + b

    then i use the values of x and y from f(x) = ln(x) and i get

    f(4) = ln(4) = .4 so x = 4 , y = 1.4

    then plugging these in the equation i get

    1.4 = 1/4(4) + b and then this equals b = 1.4 - 1 = .4 so b = .4

    now i plug all these values in and get

    y = 1/4x + .4

    but i got it wrong...can someone please tell me why and show me how i messed up...thanks
    The tangent point has the coordinates T(4, ln(4)).

    The tangent has the slope m = \frac14

    Now use point-slope-formula of the equation of a line:

    y-\ln(4) = \frac14 \cdot (x-4) . Solve for y:

    y = \frac14 x - 1 +\ln(4)
    Attached Thumbnails Attached Thumbnails Tangent lines!!-tang_anlog.jpg  
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