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Math Help - Finding Max and Min

  1. #1
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    Finding Max and Min

    Hi
    Can someone show me how to find the max and min of the following equations without using the calculator:

    1) \frac{1}{2+sin(x)}

    i done \frac{dy}{dx} and i got 1 however how do you get the minimum?

    2) \frac{1}{sin^2(x)+4}


    P.S
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  2. #2
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    Quote Originally Posted by Paymemoney View Post
    Hi
    Can someone show me how to find the max and min of the following equations without using the calculator:

    1) \frac{1}{2+sin(x)}

    i done \frac{dy}{dx} and i got 1 however how do you get the minimum?

    2) \frac{1}{sin^2(x)+4}


    P.S
    Think about \frac{1}{x} for x > 0.

    The smaller x gets, the bigger \frac{1}{x} gets, and the bigger x gets, the smaller \frac{1}{x} gets.


    So where is 2 + \sin{x} at its minimum? This is where \frac{1}{2 + \sin{x}} will be at its maximum.

    Similarly, where is 2 + \sin{x} at its maximum? This is where \frac{1}{2 + \sin{x}} will be at its minimum.



    Do the same for the second question.
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  3. #3
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    We Will Do This :

    <br />
A = \frac {1}{2+\sin x}<br />

    To Find Minimum -> Sinx=1 ( The Maximum of Sinx) So We Have :

    <br />
A = \frac {1}{2+1}=\frac {1}{3}<br />

    To Find The Maximum - > Sinx=-1 { The Min of Sinx) So We Have:

    <br />
A = \frac {1}{2-1}= 1<br />


    So

    <br />
\frac {1}{3} < A < 1<br />
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