A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must be 600 cm. In this problem you will find the base length a which will maximize the area of such a window. Use calculus to find
an exact answer.
When the base length is zero, the area of the window will be zero. There is also a limit on how large scan be: when x is large
enough, the rectangular portion of the window shrinks down to zero height. What is the exact largest value of r when this
occurs?

Largest x = ?