Using L$/2$ & $2$L$/3$ as the location of the concentrated applied moment $($measure from point A$)$ in the bottom two figures shown, find the equations for slope and defection for the simply supported beam of length L shown above $-$ verify the deflected shapes shown and find the location and maximum values of slope and deflection $($leave your answers in terms of EI$)$

L$=12$m

q$0=4$kN$/$m

C$=4$kNm

F$=11$kN