ALTDEV ALT UNDERSHOT. FLC MISUSES AUTOPLT AND MISINTERPRETS FMC DATA AND MISSES XING ALT RESTR.

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WHILE ON A ROUTINE FLT TO STT WE WERE ASKED BY NYC TO CLB TO FL410 OR IF UNABLE TO MAINTAIN FL370 AND STANDBY FOR RERTE. BOTH CAPT AND FO ARE NEW TO THIS ACFT MODEL AND AFTER SELECTING A HIGHER ALT ON CDU/FMS AND ENTERING MAX ALT SHOWED ON CDU TO BE 40.9. WE THEN NOTIFIED ATC THAT WE COULD ACCEPT FL410. WE BEGAN CLB TO FL410 AND AS WE PASSED FL399 WE NOTICED AIRSPD WAS EXTREMELY LOW (210 KIAS). WE WERE IN VERT SPD MODE ON MCP WITH ABOUT 1400 FPM SELECTED. AT THE TIME I NOTICED THE LOW SPD WE WERE 15 NM FROM OUR XING RESTR OF FL410 AT CHAMP. WE LEVELED OFF AND THEN BEGAN A SHALLOW DSCNT TO ACCELERATE. WE THEN AGAIN TRIED TO CLB; BUT AIRSPD BEGAN TO DECLINE. AFTER PASSING OUR FIX (CHAMP) AT FL399 WE DECIDED TO NOTIFY ATC. WE WERE VECTORED OFF COURSE AND LEVELED AT FL390. WE DID A 360 DEG TURN AND REINTERCEPTED CHAMPS AFTER APPROX 10 MINS OF VECTORING AT FL410. FIRST LESSON: DO NOT USE VERT SPD MODE TO CLB AT HIGH ALT AS THIS COULD LEAD TO STALL OR UPSET. SECOND LESSON: BE CAUTIOUS OF THE MAX ALT MESSAGE. THE COMPUTER IS NOT ALWAYS CORRECT. THIRD LESSON: NOTIFY ATC IN A TIMELY MANNER IF DEV IS IMMINENT.