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Weird calculus problem

  1. Jan 7, 2004 #1
    Which of the following is an equation of a curve that intersects at right angles every curve of the family y = 1/x + k where k takes all real values?
    a)y= -x b)y= -x^2 c)y= -x^3/3 d)y=x^3/3 e)y=ln x
     
  2. jcsd
  3. Jan 7, 2004 #2

    NateTG

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    Are you sure that you don't mean
    [tex]y=\frac{1}{x} + k[/tex]

    then [tex]\frac{dy}{dx}=\frac{-1}{x^2}[/tex]

    any suitable function would have the negative reciprocal slope, so
    [tex]\frac{df}{dx}=\frac{x^2}{1}=x^2[/tex]
    sp
    [tex]f(x)=\frac{x^3}{3}+C[/tex]

    and the answer is d.
     
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