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**struck** 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.