Question

Intervalele de monotonie 3x-x*3

Answer 1

[tex]f:\mathbb{R}\rightarrow \mathbb{R},f(x)=3x-x^3\\ f'(x)=3-3x^2\\ f'(x)=0\\ 3-3x^2=0\\ 3x^2=3\\ x^2=1\Rightarrow x\in \{\pm 1\}\\ f(1)=2\\ f(-1)=-2\\ \displaystyle\limit \lim_{x\to -\infty} f(x)=\infty \\ \limit \lim_{x\to \infty} f(x)=-\infty\\ \text{Dupa ce faci un tabel iti va da }\\ Pt.\ x\in(-\infty,-1),f(x)-\text{descrescatoare}\\ Pt\ x\in[-1,1) ,f(x)- \text{crescatoare}\\ Pt\ x\in[1,\infty),f(x)-\text{descrescatoare} [/tex]