i'm trying to do analysis, but the stupid case by case part is confusing me and it's keeping me away from doing calculus.(adsbygoogle = window.adsbygoogle || []).push({});

ex:

h(x) = 3x^2 - 3

h'(x) = 3(x+1)(x-1)

how did they break down h'x to analyze it?

like, for x <= -1, --> h'x >= 0 --> h is increasing

-1<x<1 --> h'x <= 0 --> h is decreasing..

etc etc....

stuff like that...how did they get h'x is greater or lesser then 0 and increasing decreasing?

also

|x| + |x+1|

how did they get x < -1 implies |x| = -x and |x + 1| = -x - 1?

i'm sure it is really simple, but i can't see it.

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# Very simple question

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