To re-approach this problem:
Assume Vi point is driven by a step voltage, the response of Vx to that step can be proved to be as shown in the blue curve. As can be seen, at the onset of the response, it is like a ramp, this ramping of Vx introduces a ramping in the drain current at node Vi, so a step in voltage results in a ramp in current, that is a clear sign of inductor.
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