The steel $($E $=200$ GPa$)$ modified cantilever beam ABC shown in Figure $1$ is loaded in B with an upwardforce of $12$ kN$.$ The second moment of area of its cross section is $1=1\mathrm{.}2\backslash$times $10\backslash$deg mm$4($a$)$ Use your preferred method to find the expression for the deflection of the beam.$($b$)$ Qualitatively sketch the deformed state of the beam, using the expressions found in part $($b$).($c$)$ Calculate all the external reactions.$($d$)$ Use the expression$($s$)$ found in part $($a$)$ to determine the deflection of points B and C$.($e$)(5$ pts EC$)$: Determine the expression for the slope $($dy$/$dx$)$ of the beam.