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Math Help - Finding tangent line of a function

  1. #1
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    Finding tangent line of a function

    Hi there -- i could use a hand with this function:

    f(x)=2x/(1+x^2)

    I'm asked to find the tangent line at x=3, and find the horizontal tangents, (where, if I remember, the tangent line = zero, correct?). I've been looking at this for a while, can't seem to move it along.

    thanks,
    Renee
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by rhunt View Post
    Hi there -- i could use a hand with this function:

    f(x)=2x/(1+x^2)

    I'm asked to find the tangent line at x=3, and find the horizontal tangents, (where, if I remember, the tangent line = zero, correct?). I've been looking at this for a while, can't seem to move it along.

    thanks,
    Renee
    f(x)=\frac{2x}{1+x^2}

    f'(x)=\frac{(1+x^2)(2)-(2x)(2x)}{(1+x^2)^2}
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  3. #3
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    Quote Originally Posted by rhunt View Post
    Hi there -- i could use a hand with this function:

    f(x)=2x/(1+x^2)

    I'm asked to find the tangent line at x=3, and find the horizontal tangents, (where, if I remember, the tangent line = zero, correct?).
    No, not "tangent line= zero". A line is not equal to a number. The slope of a horizontal line is 0.

    I've been looking at this for a while, can't seem to move it along.

    thanks,
    Renee
    Now that alexmahone has given you the derivative of the function, can you do it?
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  4. #4
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    I think so. Solving for the horizontal slope = 0...you do by setting fprime(x) equal to zero and then solving for x, correct?
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  5. #5
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    If f(x)=2x/(1+x^2) then

    f'(x)=2(1+x^2)-(4x^2)/(x^2+1)^2
    f'(x)=-2x^2+2/(x^2+1)^2

    Then, you will f'(x) of 3:

    f'(3)=-2(3)^2+2/(3^2+1)^2
    f'(3)=36+2/100
    f'(3)=19/50

    This is now the slope of the line at x=3. You can then use point-slope form to find the equation of the line tangent, but first you need to find the y coordinate using the function f(x) and finding f(3) which results in 3/5.

    Then, the equation of the line tangent to will be:

    y-3/5=(19/50)(x-3)
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