Why is the initial short-field climb below Vₓ in a Cessna 172? Short-field takeoff procedure for a Cessna 172R is


  
  Wing Flaps – 10°.
  Brakes – APPLY.
  Throttle – FULL OPEN.
  Mixture – RICH …
  Brakes – RELEASE.
  Elevator Control – SLIGHTLY TAIL LOW.
  Climb Speed – 56 KIAS (until all obstacles are cleared then $V_y$).
  Wing Flaps – RETRACT slowly after reaching 60 KIAS.
  


However, best angle-of-climb or $V_x$ at is 62-67 KIAS depending on elevation. Why is the first stage of the climb slower than $V_x$, and if the slower speed gives better performance, then why isn’t that the published figure?
The published Vx is in the clean condition (no flaps): 62. 

With the flaps down, for a short-field takeoff, Vx is 56.

This is the same reason why the stall speed (bottom of the white arc) is lower with flaps than without (bottom of the green arc)