On Fri, 4 Jan 2013 20:59:09 -0800 (PST), firstname.lastname@example.org wrote:
> --- > If y(x) = 1 / x > then y(x) > 0 when x > 0 and y(x) < 0 when x < 0. > > According to the power rule of Calculus, y'(x) = -1 / x^2. > So y'(x) is always negative. > > Are we losing information by taking the derivative?
Yes, as evidenced by the constant of integration added going the other way.
> I think the place I make a mistake is in my understanding of how r relates to x. > If everything is oriented along the x axis, aren't they the same? Or do we have > r = |x| ?