Relation between Resistor and capacitor in AM detector

In Amplitude Demodulation, the condition which the load resistor R must satisfy to discharge capacitor C slowly between the positive peaks of the carrier wave so that the capacitor voltage will not discharge at the maximum rate of change of the modulating wave (W is message bandwidth and ω is carrier frequency, in rad/sec) is
(a) RC < 1/W
(b) RC > 1/W
(c) RC < 1/ω
(d) RC > 1/ω

Correct Answer: (a) RC < 1/W

Explanation:

The discharging time constant RC must be so that it ensures the
the capacitor to discharge slowly through the load resistor R between the positive peaks
of the carrier wave, but not so long that the capacitor voltage will not discharge at the
maximum rate of change of the modulating wave, that is

RC < 1/W

Where, W is the message bandwidth. The result is that the capacitor voltage or detector
output is nearly the same as the envelope of the AM wave.