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Calculus Review - Tangent of function and find y-intercept

  1. Sep 11, 2013 #1
    1. The problem statement, all variables and given/known data
    Consider g(ξ) = [(2H)/π] arctan(ξ).
    Plot a graph of the function g(ξ).
    Imagine a line that passes through the point on the curve at ξ0 = 1.30, and which is tangent to the curve at that point. Where does the tangent line intersect the vertical axis?
    [DATA: H = 2.00 ; ξ0 = 1.30 .]


    2. Relevant equations
    y=mx+b


    3. The attempt at a solution
    Firstly I know that H=2 so I can easily simplify the question to (4/π)*arctan(ξ).

    I then want to find the slope so I take the derivative of that function and get 4/(πξ^2+π) then plug in ξ=1.3 to find the slope at that point. The result is: 0.473323

    I can also plug ξ=1.3 in to the original equation to find the y value at that point. The result is: 1.16514

    Plugging in those values to y=mx+b I get 1.16514=(.473323)(1.3)+b. The resulting y-intercept (b) is 1.89.

    Unfortunately, this is not correct! I am obviously making a silly mistake somewhere. Is anyone able to point out what I did wrong?

    Thank you!
     
  2. jcsd
  3. Sep 11, 2013 #2

    SteamKing

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    You didn't evaluate y = mx + b correctly.

    If y = 1.16514 and mx = 0.473323*1.3, then b must be less than 1.16514
     
  4. Sep 11, 2013 #3
    I really have no idea what to say. I'll start with a thank you. Sometimes the most obvious things...
     
  5. Sep 11, 2013 #4

    SteamKing

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    You're welcome. Good luck with the rest of your review.
     
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