The interval in which $y=x^2 e^{2 x}$ is increasing is

$(-\infty,-1)$ $(-1, \infty)$ $(-\infty,-1) \cup(0, \infty)$ $(-\infty, 0) \cup(1, \infty)$

$(-\infty,-1) \cup(0, \infty)$

$y=x^2 e^{2 x} ~~\Rightarrow y'=2 x e^{2 x}+2 x^2 e^{2 x}$ so $y'=0 ~~\Rightarrow e^{2 x}(2 x)(1+x)=0$ $\Rightarrow x=0,-1$ Using wavy curve method so y' > 0 for x ∈ (-∞, -1) υ (0, ∞) so y is increasing