For this case, the only force on the beam is the force at B. There will be no moment in the beam between B and C; therefore, the beam will remain straight in this region, inclined at the slope θB.
Using the formulas for a cantilever beam with a concentrated load at the free end, the deflection VB and the slope θB can be calculated by assuming a cantilever length of L/2. Since the beam is straight between B and C, the deflection at C can be computed from the deflection at B and the product of the slope at B and the distance between B and C.