OVERHANGING $[20$ pts$]$ A $16-$m long beam is supported by an $8\mathrm{.}667$ kN force @ B and a $19\mathrm{.}333$ kN force @ D$.$ The beam is subject to a $2k\frac{N}{m}$ distributed load over the first $8$ meters and a $12-kN$ point force at E $.$

Draw the shear and moment diagrams for the beam. Show your work and include the values and locations of every minimum, maximum, and inflection point.

$V\frac{?}{?}$& $M$ Diagrams $(relatedby$ calculus$)$

$V={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}w(x)dx,M={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}V(x)dx$

$w=d\frac{V}{d}x,V=d\frac{M}{d}x$