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Horizontal Tangent

  1. May 31, 2014 #1
    If the tangent is horizontal, it is where the tangent is zero. In single var. calc. that would be at max. or min. for example. I am confused about what horizontal tangent refers to when I am given a parametric equation.

    E.g. At what value of t does x=t^2 -t and y=t^2 +t have a horizontal tangent?

    The answer is -1/2 which can be found by setting y'=0. I don't understand why this happens though. As in, why dy/dt rather than dy/dx or why does dx/dt not apply? In describing the curve, what is the relationship between the two (x and y given in parametric form) that I could just only look at dy/dt?

    My first instinct was to look for dy/dx which would look something like (2t+1)/(2t-1).
    Last edited: May 31, 2014
  2. jcsd
  3. May 31, 2014 #2
    The answer to your question is pretty simple.

    [itex]\frac{dy}{dx}[/itex] =[itex]\frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/itex].

    So for [itex]\frac{dy}{dx}[/itex] to be zero, the numerator i.e [itex]\frac{dy}{dt}[/itex] must be zero. And hence the answer.
  4. May 31, 2014 #3
  5. May 31, 2014 #4


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    More accurately, if the tangent is horizontal, it is where the slope of the tangent line is zero.
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