For the loading shown above, if the bending moment equation is given

by

$EI\frac{d^{2}y}{d{x}^2}=M,x=-\frac{w_o{x}^3}{6L}+\frac{w_{o}L}{2}x-\frac{w_o{L}^2}{3}$

Assume that EI is constant, use the double$-$integration method to

determine

The name of the above beam.

The type of loading that is subject to$.$

The name of $w_o.$

The equation of the elastic curve $y=fx.$

The deflection midway between the supports $x=\frac{L}{2}.$

The maximum deflection $y_{\text{m}\text{a}\text{x}}.$

The maximum slope ${}_{\text{m}\text{a}\text{x}}.$