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Math Help - Calculus slope intersection

  1. #1
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    Calculus slope intersection

    Can someone show me how to find the points that intersect with the graph of the function f(x) = 1-x^2 and the tangent line that goes through the point (2,0).
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  2. #2
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    Quote Originally Posted by pantera View Post
    Can someone show me how to find the points that intersect with the graph of the function f(x) = 1-x^2 and the tangent line that goes through the point (2,0).
    The point is on the curve  f(x)=1-x^2 . Say the point is (a,1-a^2). The slope of the tangent line is  k=f'(a)=-2a. So the tangent line is
     f(x)=-2a(x-a)+1-a^2=-2ax+1+a^2
    The line passes through the point  (2,0) , then 0=-4a+1+a^2
    Therefore,  a= 2\pm\sqrt{3}
    Last edited by mr fantastic; September 18th 2009 at 09:24 AM. Reason: Restored original reply
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  3. #3
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    Thank you so much!
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