Solution
= Solution
Evaluating the <function> at the endpoint gives the <displacement>
$$
\Delta=y(L)
=-\frac{\rho gL^4}{8A}+\frac{FL^3}{3A}.
$$
Therefore
$$
\boxed{h_0=-\frac{\rho gL^4}{8A}},
\qquad
\boxed{h=\frac{FL^3}{3A}},
\qquad
\boxed{\Delta=h_0+h}.
$$
The force-induced displacement $h$ is a <linear map> of $F$.