Then .
This gives R_{x} = 0.62M or R_{x} = -1.62. Negative resistance is impossible, so the corrrect answer is 0.62M. This means the wiper is 62% of the way up from the bottom.
v_{s} = 0.5V: If i_{D} = 0 then v_{D} = v_{S} = 0.5V. (Can be true). If v_{D}= 1V then mA. This cannot be true: i_{D}cannot be negative. Thus, i_{D} = 0, v_{D} = 0.5V.
v_{s} = -2V: If i_{D} = 0 then v_{D} = v_{S} = -2V. (Can be true). If v_{D}= 1V then mA. This cannot be true: i_{D}cannot be negative. Thus, i_{D} = 0, v_{D} = -2V.