Question: Prove that for a uniform-cross-section beam with simple supports at the ends loaded by a single concentrated load, the location of the maximum deflection will

Prove that for a uniform-cross-section beam with simple supports at the ends loaded by a single concentrated load, the location of the maximum deflection will never be outside the range of 0.423l ≤ x ≤ 0.577l regardless of the location of the load along the beam. The importance of this is that you can always get a quick estimate of ymax by using x = l/2.

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