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Math Help - Area-minimum

  1. #1
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    Exclamation Area-minimum

    Determine the value of a at which the area, S(a), of the region enclosed by the curves y=x^2(x-2) and y=ax(x-2), is at a minimum. Assume that 0<a<2.

    First of all, I found the points of interdections, which are 0,a,2.
    And then, I did S(a), and then S'(a). Is it correct?
    Last edited by hahalol; December 27th 2012 at 11:12 AM.
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  2. #2
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    Re: Area-minimum

    Quote Originally Posted by hahalol View Post
    Determine the value of a at which the area, S(a), of the region enclosed by the curves y=x^2(x-2) and y=ax(x-2), is at a minimum. Assume that 0<a<2.

    First of all, I found the points of interdections, which are 0,a,2. <--- to be exact these values are the x-coordinates of the points
    And then, I did S(a), and then S'(a). Is it correct? <-- yes
    1. What's your result of S(a)? S'(a) and what did you get if you solve S'(a) = 0??

    2. Did you draw sketches? The smallest area is coloured in grey.
    Attached Thumbnails Attached Thumbnails Area-minimum-minarea.png  
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