### Simply supported beam: Maximum bending moment

The bending moment M at position x m from the end of a simply supported beam of length L m carrying a uniformly distributed load of w Kn m-1 is given by M = w/2 L (L-x) - w/2 (L - x)^2 Show that the maximum bending moment occurs at the mid point of the beam, and determine its value in terms of w and L.