Consider a simply supported beam of length 50 ft subjected to a uniformly distributed downward load of 10 kips/ft from x=10 ft to x=40 ft and concentrated downward loads of 100 kips at x=10 ft and x=40 ft. Determine the shear and moment diagrams from x = 0 to x = 50 and also compute the slope dv/dx and deflection v(x) from x = 0 to x = 40.