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Math Help - Basic differentiation - find increasing and decreasing intervals...

  1. #1
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    Basic differentiation - find increasing and decreasing intervals...

    I have the following question to solve but I don't seem to grasp the concept very clearly (excuse me, I am self-studying).

    For each of the following functions f(x), find f'(x), the intervals in which f(x) is decreasing, and the intervals in which f(x) is increasing.

    x^3/2 ( x - 1 ) for x > 0


    I cannot seem to get the derivative function f'(x) right here.

    This is what I reached:

    => f(x) = x^5/2 - x ^ 3/2
    => f'(x) = 5/2x^3/2 - 3/2x^(3/2 - 1)
    = 5/2x^3/2 - 3/2x^1/2
    = 5/2x^3/2 - 3/2x^1/2

    But I don't think it's right because it doesn't help me progress to find the interval where it's decreasing or increasing.

    Edit:

    I have now grouped it as the following:

    1/2x ^ 1/2 (5x - 3)

    From my knowledge, I have to solve the inequality 5x - 3 <= 0 and 5x - 3 >= 0 .. But that's not working.
    Last edited by struck; October 29th 2008 at 10:59 PM.
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  2. #2
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    Quote Originally Posted by struck View Post
    I have the following question to solve but I don't seem to grasp the concept very clearly (excuse me, I am self-studying).

    For each of the following functions f(x), find f'(x), the intervals in which f(x) is decreasing, and the intervals in which f(x) is increasing.

    x^3/2 ( x - 1 ) for x > 0 Keep this constraint in mind!


    I cannot seem to get the derivative function f'(x) right here.

    This is what I reached:

    => f(x) = x^5/2 - x ^ 3/2
    => f'(x) = 5/2x^3/2 - 3/2x^(3/2 - 1)
    = 5/2x^3/2 - 3/2x^1/2
    = 5/2x^3/2 - 3/2x^1/2

    But I don't think it's right because it doesn't help me progress to find the interval where it's decreasing or increasing.

    Edit:

    I have now grouped it as the following:

    1/2x ^ 1/2 (5x - 3)

    From my knowledge, I have to solve the inequality 5x - 3 <= 0 and 5x - 3 >= 0 .. But that's not working.
    All your considerations and all your calculations are correct. You only have to add to your inequalities the condition x > 0

    Then you'll get:

    f(x)\ is\ \left\{\begin{array}{l}decreasing\ if\ 0<x\leq\dfrac35 \\ increasing\ if\ x > \dfrac35 \end{array}\right.

    I've attached the graph of the function.
    Attached Thumbnails Attached Thumbnails Basic differentiation - find increasing and decreasing intervals...-incr_decrwurzel.png  
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