For the beam shown below, please:

$(1)$ Calculate the vertical reactions at the supports $"$A$"$ and $"$B$".$

$(2)$ Write the equations for the internal shear and the internal moment in terms of $"x".$

$(3)$ Draw the shear force diagram $($SFD$),$ and the Bending moment diagram $($BMD$).$

$(4)$ Determine the location and magnitude of the $M_{\text{m}\text{a}\text{x}}.$