For the beam below, $E=29,000$ksi and $I=291i{n}^4.$

a$.$ What are the boundary conditions for the beam?

b$.$ The moment equation is $M(x)=(-\frac{1}{18}{x}^3+13\mathrm{.}5x-81)kip*ft.$ Write the equation for the curvature of the beam as a function of $x.$

c$.$ Find the equations for slope and deflection. Solve for the constants of integration.

d$.$ Sketch the deflected shape and label:

i$.$ The maximum deflection

ii$.$ The maximum slope

iii. The deflection at $x=4\mathrm{.}5ft$

iv$.$ The slope at $x=4\mathrm{.}5ft$

e$.$ Calculate the values for the deflections and slopes you labeled in part $3$d$.$