Calculus optimization scenario involving a window shaped like a semicircular arch atop a rectangle.[br][br]For a given perimeter of this window, use calculus to find the dimensions (diameter of semicircle [b]x[/b], height of rectangle [b]y[/b]) that would maximize the window area. Use this construction to verify your answer and visualize the geometry. Drag the large [color=#0000ff]point[/color] in the left graphics view to adjust the size of the window. For keyboard control, select the [color=#0000ff]point[/color] and use the arrow keys to adjust, also pressing shift key for finer control.[br][br]"Lengths" toggle displays length values to three decimal places in the left graphics view.[br][br]"Area" toggle graphs area as a function of [b]x[/b] in the right graphics view.[br][br]"Window type" button toggles between three window designs, including all displayed segments in the calculation of perimeter:[br][list=1][*]outer edges only[br](Use this if you're my student checking a homework exercise, even though textbook graphic shows a horizontal interior crossbar)[/*][*]outer edges plus one horizontal interior crossbar[/*][*]outer edges plus two horizontal one one vertical interior crossbars[/*][/list][br]Click/touch icon in lower-right corner of graphics view to display full-screen.