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Decreasing/concave upward: xlnx

  1. Apr 18, 2010 #1
    1. The problem statement, all variables and given/known data

    a) On what interval is f(x) = xlnx decreasing?
    b) On what interval is f concave upward?

    2. Relevant equations

    d /dx(lnx) = 1 / x
    d /dx[f(x)g(x)] = f(x)g'(x) + g(x)f'(x) (Product Rule)

    3. The attempt at a solution

    a) f'(x) = (x)d/dx(lnx) + (lnx)d/x(x)
    = x * 1 / x + lnx
    = lnx

    According to lnx graph, f(x) decreasing when 0 < x < 1

    b) f''(x) = 1 / x

    According to 1 / x graph f concave upward when x < 0
  2. jcsd
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