Find the critical value of the load P in Fig. P11.41 if both ends of the beam...

Find the critical value of the load P in Fig. P11.41 if both ends of the beam are simply supported. Let L₁ = L/4 and L₂ = 3L/4. Employ the method of finite differences by taking the nodes at x = 0, x = L/4, x = L/2, and x = L.