14. The shaded right-angled triangle in the diagram below has one vertex at (0,0) , a second at the point (11,0) and a third at the point (a,b) which lies on the line with equation y = 1_' The coordinates a andb are positive, real numbers. a a z a. Show that the area of the shaded triangle can be expressed as E E b. Find the maximum area of the shaded triangle as well as the value of a for which this maximum occurs