The force exerted by a compression device is given by $F\left(x\right)=kx\left(x-l\right)$ for $0\le x\le l$ where $l$ is the maximum possible compression, x is the compression and k is a constant. The work required to compress the device by a distance d will be maximum when

For W to be maximum, dW/dx=0;

$\text{ i.e., }F\left(x\right)=0\Rightarrow x=l,x=0$

Clearly, for $d=l,$the work done is maximum.

Alternate Solution : External force and displacement are in the same direction.

$\therefore$ Work will be positive, Continuously, so it will be maximum when displacement is maximum.