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
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Erdos
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