PLEASE LABEL EACH SECTION CLEARLY $($a b and c$)$

Consider the beam below of length $2L$ and constant flexural rigidity $EI.$

a$.$ Determine the equations for the elastic deflection $v(x)$ along the entire beam using the Double Integration Method. $($Note: You will need to use a continuity condition to solve this problem.$)$

b$.$ Determine the deflection at the end of the beam $($point C$).$

c$.$ How would the deflection at the end of the beam $($point $C)$ change if the length between A and $B$ remains the same, but the length of the cantilever $($B to C$)$ increases from $L$ to $2L?$ Why is this the case?