This may be a beginner question, but I really want to understand this good and thorough.
I have this sine function, withing the interval $-3 ≤ x ≤ 3$
$$f(x)=\frac{\sin (\pi x)}{\sin(2\pi x)}$$
My question is regarding local maximum and minimum values wich i assume this function does not have, as all $f'(x)=0$ are undefined? In the same manner this function would also not have a horizontal tangent?
(as far as i understand its possible to transform the function using trig identities, but the questions above is regarding the function in it's original form.)
Would be really greatful for any help.
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