Is this homework? Then it should have been posted in the homework section.
Ignore the battery (remove from the circuit). Calculate the voltage at point A. Replace the voltage at point A by the battery's voltage minus the diode's drop if the voltage as calculated in the first step is lower than the voltage from the battery (minus the diode's drop).
With some caution you could also use this approach:
Apply the
superposition theorem to the circuit.
First "turn off" the AC source by replacing it with a short circuit. Calculate the output.
Second "turn off" the battery by replacing it with a short circuit. Calculate the output.
The sum of both calculations is the circuit's behaviour.
Since the superposition theorem is only valid for linear circuits but you have a diode (nonlinear element) in your circuit, you will have to make different calculations for the diode being conductive or non-conductive. For the final result superimpose the different results piecewise. The graph on the right of the schematic you provided gives you the necessary clues (linear - sinusoidal - linear).