SOLUTION: Rectangle QRST between curve {{{y=-x^2+4}}} and {{{y=x^2-4}}}. Let P be the point of intersection of the side QT and the x-axis. Let α be the length of the perimeter of this r

Question 750024: Rectangle QRST between curve and . Let P be the point of intersection of the side QT and the x-axis. Let α be the length of the perimeter of this rectangle. We are to find the x-coordinate of the point P where α is maximized and also to find the maximum value of α. P(x,0), where 0 Therefore, when x=(A), α is maximized and its maximum value is (B)
solve for A and B
((this is the picture of the graph http://i44.tinypic.com/30sk9ir.jpg)
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Both curves and the rectangle QRST are symmetrical with respect to the y-axis.
TI'll call the coordinates of P (a,0), to distinguish that x-coordinate value from the variable .
The x-coordinates of points R and S are the same .
The y-coordinate of points Q and R, on curve is .
The y-coordinate of points S and T, on curve is .
The width ST (or QR) of the rectangle is .
The height RS (or QT) of the rectangle is .
The perimeter of the rectangle is

is a quadratic function in
It's maximum is at
because a parabola such as has a vertex as
The equation in vertex form would be

So the maximum value of happens at
and the maximum value of is
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SOLUTION: Rectangle QRST between curve {{{y=-x^2+4}}} and {{{y=x^2-4}}}. Let P be the point of intersection of the side QT and the x-axis. Let &#945; be the length of the perimeter of this r

SOLUTION: Rectangle QRST between curve {{{y=-x^2+4}}} and {{{y=x^2-4}}}. Let P be the point of intersection of the side QT and the x-axis. Let α be the length of the perimeter of this r