For boeing a/c (757/67/47), two questions:
1) In flight with autothrottle on, an engine is shut down. If A/T is kept on, will the servo move the throttle lever of the shut engine like it does with the working one?
2) A/T in speed mode, in a climb. Pilot increases speed bug on MCP. How will react A/T system? Should it make a quick movement of the levers up to max power for CLB mode, until speed is near to be captured, and retard them back until speed is stabilized; or should it make a slow/smooth movement, letting speed increase steady to the point of being captured?