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Thread: Maximun are of rectangle

  1. #1
    Junior Member
    Oct 2009

    Maximun are of rectangle

    find the maximun are of rectangle if his points are O(0,0) A (x,0) C(0,y) and B is in the graph of function $\displaystyle e^(-x)$

    i tried this way:
    S= x * y = x * e^(-x)
    then i found the first derivative, then found the point wich the funcion has extremum (x=1) then i found the second derivative and pluged the extrem point x=1 into the function witch was now <0
    now the maximum area is S=1*e^(-1)
    am i right ? if isn't how should i solve this ?
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  2. #2
    Senior Member
    Feb 2010
    If x is required to be positive, you are correct, though you need to show that the rectangle does not become larger as you go to 0 or $\displaystyle +\infty$. If x can be negative, the retangle can be arbitrarily large.
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