Can somebody please help me out with this question? I have done most of it and I just need to do the final part which is:

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Given the equation:

$\displaystyle y = \frac{a+bsinx}{b+asinx}$

where $\displaystyle 0<a<b$

Find the maximum and minimum values of y.

I can give you the following information I figured out and hopefully, that can help you help me:

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First, I discovered that the graph does NOT have any vertical asymptotes

Also, differentiating and simplifying it gave me $\displaystyle \frac{dy}{dx} = \frac{(b^2 - a^2)cosx}{(b+asinx)^2}$

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First, I believe that I may have to make $\displaystyle \frac{(b^2 - a^2)cosx}{(b+asinx)^2} = 0$

Now I'm stuck.

If you could help me out, it would be greatly appreciated. Thanks!