<s>[INST] Showing that $3x^2+2x\sin(x) + x^2\cos(x) > 0$ for all $x\neq 0$ I got this question:
Show that for all $x\neq 0$, $3x^2+2x\sin(x) + x^2\cos(x) > 0$
I tried to show it but got stuck.
 [/INST] If $x<0$ then
$$\sin x<-x\implies 2x\sin x>-2x^2$$
and
$$\cos x\ge-1\implies x^2\cos x\ge-x^2$$
and so
$$3x^2+2x\sin x+x^2\cos x>3x^2-2x^2-x^2=0\ .$$
The case $x>0$ is   similar, even a bit easier. 
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