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Homework Help: Can the line x=0 be differentiable?

  1. Apr 27, 2005 #1
    can the line x=0 be differentiable?

    the slope would be infinity right? so does that mean it is differentiable?
     
  2. jcsd
  3. Apr 27, 2005 #2

    cepheid

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    x = f(y) = 0 is a function, and [itex] \frac{dx}{dy} [/itex] is certainly defined. But graphing that in the traditional manner (indep. variable on the horizontal axis), of course gives a horizontal line of slope 0.

    The problem with your example the way you were thinking about it is that it doesn't even represent a function of x! Think about it...you can plug only x = 0 into this "function", and when you do, any conceivable value of y is allowed. Is that a function?

    In any case, the slope of a vertical line is undefined.
     
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