A straight prismatic beam AD has a rectangular cross$-$section with width $\backslash ($ b $\backslash )$ and height $\backslash ($ h $\backslash ).$ Its total length is $\backslash (4$ l $\backslash ).$ Its Young's modulus is $\backslash ($ E $\backslash ).$ The beam is subjected to distributed load $\backslash ($ q $\backslash )$ per unit length, as shown in the figure below.

$(1)$ Please use the energy method to determine the deflection, $\backslash ($ v $\backslash ),$ at $\backslash ($ x$=$l $\backslash ).$

$(2)$ Please use the energy method to determine the slope of the deflection curve, $\backslash ($ v$^\{\backslash$prime$\}\backslash ),$ at $\backslash ($ x$=3$ l $\backslash ).$