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Tangent Line

  1. Jun 6, 2005 #1
    Find the point(s) (x,Y) at which the tangent line to x^2+4y+22=y^2+10x is horizontal.
  2. jcsd
  3. Jun 6, 2005 #2


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    What does it means when the tangent line is horizontal? what does the first derivative has to do with the "tangent"?
  4. Jun 9, 2005 #3
    Differentiating this equation implicitly with respect to x yields 2x-10/2y-4. Thus we see that 2x-10=0 (2y-4 can't equal zero, that would be undefined) From here x=5. So the point is P(5,y). set x=5 in the original equation, solve for y and there you got the y. This turns out that that y has two values for x=5, and those being 1 and 3.

    Btw, tangent comes from the latin word tangens, which means touch. So a tangent line touches a curve at just one point. And the derivative of the curve at that point gives us the slope of the tangent line.
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