Finding only one real root for a function

Let $h(x)=\frac{9}{2} x-4sin(x)$, Show that h(x) has exactly one real root.

My professor also gave a little "hint"
(This one real root should be really easy to find. In fact you shouldn't have to "solve" anything to find it. All you have to show is there cannot be another one.)

Would I use the Intermediate Value Theorem? I'm not really sure where to start :(

I already found h'(x) which is $\frac{9}{2} -4cos(x)$ 
I also tried to set h(x) equal to 0 and got $\frac{8}{9} sin(x)$, I'm not sure if any of those are helpful or not. I'm probably overthinking this entire problem LOL

Thanks in advance


Answers can be viewed only if
  1. The questioner was satisfied and accepted the answer, or
  2. The answer was disputed, but the judge evaluated it as 100% correct.
View the answer
Erdos Erdos
The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to 50% commission on every question your affiliated users ask or answer.