So I got the answer to this question but it seems a little iffy. If someone could just double check my work, that would be wonderful.

I am not sure if this matters, but the level of math in this question is AP Calc-AB.

Find the area of the largest rectangle (with sides parallel to the coordinate axis) that cna be inscribed in the region enclosed by the graphs and .

there is a picture, but it isn't that helpful.

x.doc

so this is what i did. since we are looking for the largest area, i started with the area formula. . I labeled each the distance from the y axis x. and since the rectangle is touching each graph, these are the x coordinates. for the bottom right hand corner and for the top right hand corner. So I know and =the distance between and . So i used the distance formula;

so then i did i got the derivative and i found the zeros and one was negative so the only possibility was x=1.732.

so x=1.732 will optimize the rectangle, correct?