The beam supports a uniform load $w.$ There is a support located a distance $x$ from each end of the beam.

Questions:

If $x=0\mathrm{.}12L,$ the maximum $($absolute value$)$ bending moment in the beam is

$w{L}^2$

If $x=0\mathrm{.}37L,$ the maximum $($absolute value$)$ bending moment in the beam is

$w{L}^2$

By carefully choosing the distance $x$ you can minimize the maximum $($absolute value$)$ bending moment in the beam.

You would do this by choosing $x=$

L$.$

For this value of $x$ the maximum $($absolute value$)$ bending moment in the beam is

$w{L}^2$