Maximum power transfer: the question

This is the circuit from the lecture, running. Change it and the answer changes with it:

• Click any component value to edit it, or drag components to rearrange.
• The wrench opens a step-by-step analysis — it chooses a reference node and writes the node equations. Leave its Domain on the DC operating point for this deck.
• The crosshairs probe reads a node voltage or a branch current, so you can check any intermediate result rather than only the final answer.

Symbols, so nothing simulates yet. Put in $V_{Th} = 6$ V and $R_{Th} = 5$ k, then step $R_L$ through 1 k, 5 k and 10 k and watch the load power rather than the load voltage: 1 mW, 1.8 mW, 1.6 mW. The voltage climbs the whole way; the power does not.