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Math Help - Maximum and minimum value of function?

  1. #1
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    Maximum and minimum value of function?

    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:

    ================================

    Given the equation:

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

    where 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:

    ----------------

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

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

    ----------------

    ================================

    First, I believe that I may have to make \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!
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  2. #2
    MHF Contributor
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    I'm going to assume your derivative calculation and simplification are correct. Then yes you are right the next step is to look where this expression equals 0 or is undefined. So,

    The cosine function is periodic and will hit 0 an infinite amount of time. Generally \cos(x)=0, x=\frac{k \pi}{2}, where k is any odd integer.

    The other non-trivial time f'=0 is when b^2-a^2=0 This means that either a=0 or one of the terms has to be negative. Since both cases are not possible, this solution doesn't hold with the constraints.

    The derivative is undefined when b+a\sin(x)=0 (the squared doesn't matter here). So we're looking for when \sin(x)= -\frac{b}{a} And since b>a always, that means b/a is greater than one and this has no solutions.
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  3. #3
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    Thank you very much for your help
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