# Prove that $x \sin x$ and $x^3 + x + 1$ intersect

I've been working on some problems and this particular one caught me off guard. Just by reading it, I thought it was a very simple problem where I equate the two equations and solve for $x$. However, my attempt was futile and I am stuck.

Prove that the graphs of the functions $y = x \sin x$ and $y = x^3 + x + 1$ intersect.

Hint: Check the values at x = -1, and x = 0

Any hints or help are greatly appreciated! Thank you for your time.

-
To find points of intersection, equate the two equations and solve for $x$. –  Mhenni Benghorbal Dec 8 '13 at 3:56
@Mhenni, I would like to see you solve $x\sin x=x^3+x+1$ for $x$. –  Gerry Myerson Dec 8 '13 at 3:57
Consider $f(x) = x \sin x - (x^3+x+1)$ and apply the hint. –  Macavity Dec 8 '13 at 3:58
@GerryMyerson: I leave it to you you to work it out :). –  Mhenni Benghorbal Dec 8 '13 at 3:59