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Interval increasing/decreasing

  1. Apr 12, 2010 #1
    1. The problem statement, all variables and given/known data

    ln(3x+5) Determine intervals on which the function is increasing, decreasing, concave up, and concave down.

    2. Relevant equations

    3. The attempt at a solution

    So I did f '(x) = 3/3x+5
    this gives me 3x+5 = 0, and I get x = -5/3 (point where the y is zero)

    Now, I did f '' (x), and got -3/(3x+5)^2
    this gives me (3x+5)(3x+5), i did a number line test, with the only value -5/3, and anything below -5/3 is negative, and before -5/3 is positive

    this gives me that, the function is decreasing after -5/3, and increasing after -5/3.

    Now what about the concavity?
  2. jcsd
  3. Apr 12, 2010 #2


    Staff: Mentor

    No, f'(x) is never zero.
    You're not taking into account the domain of the original function, f(x) = ln(3x + 5). This function is defined only for x such that 3x + 5 > 0. The first and second derivatives have the same domain.

  4. Apr 12, 2010 #3
  5. Apr 12, 2010 #4


    Staff: Mentor

    Look at the sign of f''(x), which by the way is not equal to 3/(3x + 5)^2. Keep in mind what the domain is.
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