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This problem deals with functions defined by f(x) = x^3 - 3bx with b > 0.

  1. Feb 6, 2010 #1
    (a) Find the x- and y-coordinates of the relative maximum points of f in terms of b.
    (b) Find the x- and y-coordinates of the relative minimum points of f in terms of b.
    (c) Show that for all values of b > 0, the relative maximum and minimum points lie on a function of the form y = -ax3 by finding the value of a.

    (a)

    f(x)=x3-3bx
    f'(x)=3x2-3b=0
    x2=b
    x=+/-sqrt(b)

    when x=-sqrt(b),
    f(x) = y = -b3/2 - 3b(-b1/2)
    (x,y) = ( -sqrt(b) , 2b3/2) f has a maximum

    (b)

    when x=sqrt(b),
    f(x) = y = b3/2 - 3b(b1/2)
    (x,y)=(sqrt(b),-2b3/2) f has a minimum

    (c)

    I'm not sure. Can someone help me with (c)?

    Ok, i attempted each part. Did i do anything wrong?
     
  2. jcsd
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