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Math Help - Did I do this problem correctly (equation of the line tangent)

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    Did I do this problem correctly (equation of the line tangent)

    the problem goes as so...find the equation of the line tangent to f(x) = -1/x at the point (3, -1/3). Using the four-step process to find f'(x), I got:

    f'(x) = 1/x^2

    then using that derivative, i found the slope of the tangent line as f'(3) = 1/3^2 or 1/9.

    thus, f(x) is f(3) = -1/3

    lastly using y-y0=m(x-x0) i got y + 1/3 = 1/9(x-3)

    solving that i got 1/9x -.6 (repeating)



    does that sound right? thanks
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    Quote Originally Posted by calcconfused View Post
    the problem goes as so...find the equation of the line tangent to f(x) = -1/x at the point (3, -1/3). Using the four-step process to find f'(x), I got:

    f'(x) = 1/x^2

    then using that derivative, i found the slope of the tangent line as f'(3) = 1/3^2 or 1/9.

    thus, f(x) is f(3) = -1/3

    lastly using y-y0=m(x-x0) i got y + 1/3 = 1/9(x-3)

    solving that i got y=1/9x -.6 (repeating)



    does that sound right? thanks
    Correct (be aware of the red addendum)

    You could also write -\frac 23 instead of -0.6.....
    it'd be better
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