The bending moment, M , at position x meters from the end of a simply supported beam of length l meters carrying a uniformly distributed load of w kN meters^-1 is given by:

M = w/2 l (l-x) - w/2 (l-x)^2

Show, using the above expression, that the maximum bending moment occurs at the mid-point of the beam and determine its value in terms of w and l.