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Response Details:
You need to find the first derivative:
f '(x) = 12x3 -12x2 -24x
f '(x) = 12x (x2 - x - 2)
f '(x) = 12x (x + 1) (x - 2)
Let f '(x) = 0
We have x = 0, x = -1 or x = 2
Follow this chart
There is a method to make this chart really fast but it is quite long to explain. So the most practical way is to plug in the points between roots to see if it is positive or negative (this only use for polynomial function, it is different for rational function)
As you know, when f '(x) > 0, it means the slope greater than 0, so f (x) is increasing. The same when f '(x) < 0, f (x) is decreasing
So the answer is
Decreasing: (-∞, -1) U (0, 2)
Increasing: (-1, 0) U (2, +∞)
Hope this helps and please rate me as I took time to solve it, thank you
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