Let's say that when you turn the frequency knob on your radio you're changing the capacitance of a variable capacitor. When the capacitance is set to 20 pF you hear WBUR, BU's National Public Radio station at a frequency of 90.9 MHz.
What is the inductance of the tuning circuit?
If you want to tune the radio to WBOS at 92.9 MHz instead, should you increase or decrease the capacitance in the circuit?
To increase the resonance frequency you need to decrease the capacitance.
Switching from AM to FM means bringing in a different inductor. Is the inductance of the inductor for the AM band larger than or smaller than the inductance of the inductor for the FM band?
The AM band is in kHz (e.g., 1250 kHz), at a lower frequency than the FM band. Switching to AM means switching to lower resonance frequencies - that needs a larger inductance.