rencider the loaded beam shown.

Solving these six equations with six unknowns:

$C_1=54000,C_2=-675000$

$D_1=81000,D_2=-810000$

$K_1=225000,K_2=-2160000$

Drawing the FBD of the beam and applying static equilibrium equation results in solving for the reaction forces $R_B$ and $R_C.$ The load diagram

$8$#$/$ft

Calculate deflection at A

$\sqrt[\phantom{2}]{(0)}$

$-40x^3+C,x+C_2$

Calculate deflection at D

Calculate slope at A

Calculate slope at B