Finding Intervals for Increasing and Decreasing Functions of a Cubic Equation

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hi, I'm not good at math at all. and I'm not sure how to finish this equation. any help would be appreciated. Thanks.



I need to find the intervals of where the function is increasing and decreasing.

f(x)= 2x3 - 5x2 - 4x + 2
 
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Well first you need to differentiate it. What do you think you should do after that?
 
You need first to construct a table for that and find the roots of the equation and its differentials.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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