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Determine the intervals where the function is increasing and where it is decreasing.
f(x)=(ln(x))/x

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  2. Determine the intervals where the function is increasing and where it is decreasing.
    f(x)=(ln(x))/x

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  3. Look for places where the derivative f'(x) is positive or negative.

    f'(x) = (1 - lnx)/x^2

    f'(x) is positive where lnx < 1

    lnx = 1 at x = e

    at x>e, the derivative is negative and the function decreases.

    The function f(x) is not defined for x = 0 or x<0

    Check:

    at x = 0.1, f(x) = -2.303
    at x = 0.5, f(x) = -1.386
    at x = 1, f(x) = 0
    at x = 2, f(x) = 0.3466
    at x = e = 2.71828, f(x) = 0.3686
    at x = 3, f(x) = 0.3662

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