Answer
See the detailed answer below.
Work Step by Step
We have 2 stages of motion which are from $y=0$ m to $y=1$, and from $y=1$ m to $y=5$ m.
It is obvious that the two stages are having constant slopes since they are represented by straight lines.
$${\rm Slope}=\dfrac{\Delta U}{\Delta y}$$
So we need to find the slope of each stage:
$${\rm Slope}_1=\dfrac{ U_f-U_i}{ y_f-y_i}=\dfrac{60-0}{1-0}=\bf 60\;\rm J/m$$
$${\rm Slope}_2=\dfrac{ U_f-U_i}{ y_f-y_i}=\dfrac{0-60}{5-1}=\bf -15\;\rm J/m$$
We know that the force is given by
$$F_y=\dfrac{-dU}{dy}=-{\rm Slope}$$
Thus,
- At $y=0.5$ m, which is in the first stage, the force is
$$F_y=-{\rm Slope}_1=-(60)=\color{red}{\bf -60}\;\rm N$$
- At $y=4$ m, which is in the second stage, the force is
$$F_y=-{\rm Slope}_2=-(-15)=\color{red}{\bf 15}\;\rm N$$
