Largest rectangle between two parabolic curves

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Thu, 08/26/2010 - 16:15
mico
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Joined: Mar 17 2010

the upper and lower vertices of a rectangle lie on the curves x^2=5-y and x^2=4y respectively. the sides of the rectangle are parallel to the coordinate axes. find the maximum area of the rectangle.

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Change the title to reflect the topic of this discussion and for easy searching of information. The old title is "calculus...".


 


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Fri, 08/27/2010 - 07:03
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Dario
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Joined: Apr 24 2009
Re: calculus...

Rectangle is symmetric with the y-axis.
Length = 2x
Width = (y of x^2=5-y) - (y of x^2=4y)
Area = Length times width
differentiate the are in x and equate to zero
solve for x, my answer for x is 2/sqrt(3)
Use the value of x to solve for maximum area of rectangle.

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