In Figure $2,$ for the beam and loading shown:

$($a$)$ Determine the reaction forces at support A and $C[6\%]$;

$($b$)$ Determine the equation of the elastic curve $[20\%]$;

$($c$)$ Determine the deflection at point $B[8\%]$;

$($d$)$ Determine the slope at point $C[8\%]$;

$($e$)$ Determine the deflection at point $D[8\%].$

Ps$.$ i have a little idea that the solution might be related to the elongation of point c equals to $0$ but i dont know where to start. i would appreciate it if question b is explained thoroughly.