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.