P$7\mathrm{.}36$ For the beam and loading shown,

$($a$)$ Use discontinuity functions to write the expression for $w(x).$ Include the beam reactions in this expression.

$($b$)$ Integrate $w(x)$ twice to determine $V(x)$ and $M(x).$

$($c$)$ Use $V(x)$ and $M(x)$ to plot the shear$-$force and bending$-$moment diagrams.

FIGURE P$7.36$