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Math Help - Polar curves Maximum and minimum.

  1. #1
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    Polar curves Maximum and minimum.

    I do not understand how to find the maximum and minimum.

    Find the maximum and minimum point form the pole.

    a) r=6cos(x)

    b)r=3-6sin(x)

    I can find the answer on my calculator I believe but do not know how to do this by hand. Please help.

    Thank You.
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  2. #2
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    Hey,

    First realize that the functions you are dealing with are the cos/sin functions. Do the following (i haven't specified an interval):

    1) Differentiate the function, i.e. find r'(x)

    2) Solve the equation r'(x)=0. You may get several x-values, depending on the interval you are considering.

    3) Find r'(x) for values greater and smaller than the x value found in 2). From the found r'(x) in this part you can establish where the function increases and where it decreases.

    4) Hence if the function increases up until x=k and then starts decreasing you'll know that at x=k you have the maximum function-value.
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  3. #3
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    I haven't learned how to differentiate yet? Is there another way?
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  4. #4
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    Hello, IDontunderstand!

    By the way, polar expressions are always written in terms of \,r and \,\theta.


    Find the maximum and minimum points from the pole.

    . . a)\;r\:=\:6\cos\theta

    . . b)\;r\:=\:3-6\sin\theta

    Without Calculus? .It can be done, but it takes a bit of Thinking.
    Can you handle that?


    (a)\;r \:=\:6\cos\theta

    We know that \cos\theta ranges between -1 and +1.

    The maximum value of \,r occurs when \cos\theta = +1
    . . That is, when \theta = 0.
    Hence, a maximum occurs at (6,\,0)

    The minimum value of \,r occurs when \cos\theta = \text{-}1.
    . . That is, when \theta = \pi.
    Hence, a minimum occurs at (-6,\,\pi)



    (b)\;r \:=\:3 - 6\sin\theta

    We know that \sin\theta ranges between -1 and +1.

    The maximum value of \,r occurs when \sin\theta = \text{-}1
    . . That is, when \theta = \frac{3\pi}{2}
    Hence, a maximum occurs at \left(9,\:\frac{3\pi}{2}\right)

    The minimum value of \,r occurs when \sin\theta = +1.
    . . That is, when \theta = \frac{\pi}{2}
    Hence, a minimum occurs at \left(-3,\:\frac{\pi}{2}\right)

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