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Math Help - Finding coordinates on a tangent line.

  1. #1
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    Finding coordinates on a tangent line.


    I apologize if the image is a little hard to see. But that's the image given in the problem and it goes like this:

    "The function has f(4) = 25 and f'(4) = 1.5. Find the coordinates of the points A, B, and C."

    In case you can't see it, along the x-axis, point C is at 3.9, point A is at 4, and point B is at 4.2.

    Any help on how to do this, please?
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  2. #2
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    Equation of the tangent line at (a,f(a)):

    y = f ' (a) (x-a) +f(a)

    y= 1.5 (x-4) + 25

    you should now be able to answer the question
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  3. #3
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    Quote Originally Posted by Rumor View Post

    I apologize if the image is a little hard to see. But that's the image given in the problem and it goes like this:

    "The function has f(4) = 25 and f'(4) = 1.5. Find the coordinates of the points A, B, and C."

    In case you can't see it, along the x-axis, point C is at 3.9, point A is at 4, and point B is at 4.2.

    Any help on how to do this, please?
    As f(4) = 25 and we're given f '(4) ==> (4,25) is the tangency point and thus it belongs to the tangent line of f at (4,25) ==> this line passes thorugh (4,25) and its slope is f '(4) = 1.5, so its equation is:

    y - 25 = 1.5(x - 4) ==> y = 1.5x + 19

    Well, now just plg in x = 3.9 and x = 4.2 to find out the y-coordinate of points C and B, resp.

    Tonio
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