A beam is supported at the two ends and is uniformly loaded. The bending moment `M` at a distance `x` from one end is given by `M=(W L)/2xx-W/2x^2` Find the point at which `M` is maximum in each case.

Explanation

A beam is supported at the two ends and is uniformly loaded. The
bending moment `M`
at a distance `x`
from one finish is given by
`M=(W L)/2xx-W/2x^2`
we have to search out the point at that`M`
is maximum in each case.
so,`M=(W L)/2xx-W/2x^2`
differentiating the above equation, we get,
`(dM)/(dx)=(WL)/2-2W/2x`
now,equating `(dM)/(dx)=0`
`=>(WL)/2-2W/2x=0`
`=>(WL)/2=2W/2x`
`=>x=L/2`
again differentiate on each side we have a tendency to get,
`(d^2M)/(dx^2)=-2W/2`
`=-W<0`
Therefore , f(x) is maximum when `x=L/2`