Question

решить неравенство f'(x)>0 f(x)=2x^3+6x^2

Answer 1

$f(x)=2x^3+6x^2$
$f'(x)=(2x^3+6x^2)'=6x^2+12x$
$f'(x) textgreater 0$
$6x^2+12x textgreater 0$
$6x(x+2) textgreater 0$
$6x=0$   $x+2=0$
$x=0$     $x=-2$

-----+-----(-2)----- - ----(0)------+------
/////////////                        ///////////////
$x$ ∈ $(-$ ∞ $;-2)$ ∪ $(0;+$ ∞ $)$