What is meant by "capacitors try to try to maintain voltage at a constant level"
capacitors are kind of like rechargable batteries.  if you increase the voltage feeding them they charge up some, they absorb some of the difference between their voltage and the voltage source, if the voltage source drops they give some back to the circuit, esp if the voltage source goes away all together.

it goes like C dv/dt using calculus the capacitance times the change in voltage over time.  doesnt matter if that change in voltage is from 10 to 100 or 3 to 7 or 27 to 13 volts.

When the source has a step change, the capacitor does not instantly step, that is what C dv/dt tells you, there is some period of time for that capacitor and that step change for the capacitor to store up (or release) enough charge to match the source, if it can.  if your step changes are far enough apart then you can forget about step changes before, but if you change it fast enough it may not have caught up before it has to change again a fast enough square wave on the source and the capacitor makes it look like a sawtooth or like sharks fins...

the "resistance" is this capacitance times the change in voltage over time.  be it an increase or decrease.