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. 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.