potential dividers in physics

the minimum voltage is what you have to calculate so I don't know

Well it's guaranteed that it cant be above 10V and in figure 1 that's possible when the variable resistor is turned down to 0 Ohm.

You can use V=IR on the variable resistor to confirm that the voltage across a 0 Ohm resistor is always 0V at any current... So the full supply voltage has to be across the fixed resistor in eries with it.