A cantilever beam with a uniform circular cross$-$section $($constant moment of inertia I$)$ is subjected to two point loads. The beam is fixed at A and has the following setup:

$$ Point load PB acts downward at point B$,$ located at a distance L from A

$$ Point load PC acts downward at point C$,$ located at a distance $2$L from A

$$ The modulus of elasticity of the material is E

$$ The beam has a constant moment of inertia I

Tasks:

a$)$ Derive expressions for the slope at B and C$.$

b$)$ Derive expressions for the deflection at B and C$.$