A quadrilateral is called cyclic if its corners lie on the circumference of a circle. An example is shown

Question

below left: the circle has radius 5
The area A of the quadrilateral for different x values is plotted on the right. It can be calculated that
this curve has derivative:
dA/dx=48x^2 + (x3 − 50x)*sqrt(100−x^2)−2400/very complicated equation

(a) Show that the quadrilateral has maximum area when x=sqrt(50)
(b) At which x values does the quadrilateral have minimum area?
(c) The curve has minima at x = −6 and x = −8. What do these minima mean, in terms of the area of the quadrilateral?