(a) Suppose that a beam is fixed at its ends x = 0 and x = L. Show that its shape is given...

(a) Suppose that a beam is fixed at its ends x = 0 and x = L. Show that its shape is given by

(b) Show that the roots of y′(x) = 0 are x = 0, x = L, and x = L/2, so it follows (why?) that the maximum deflection of the beam is

one-fifth that of a beam with simply supported ends.