Newcrew & davidjh,
as OS stated, there will be a Vx for both F10 and F0. Therefore, the POH may state that you should perform Vx climb at F10 - under the assumption that the typical C150/152 operation with Vx will be performed with the intention of clearing close-in obstacles, where F10 will give you a better net gradient from brake release till clear of a, say, 100 ft. obstacle. So the POH in this case "mind-reads" the pilot.
Therefore, from a procedure point of view, Vx climb is performed with F10 (Vx10). But from a pure performance point of view, the gradient obtained with F0 is greather than with F10. A review of excess thrust curves for the two configs will confirm this
So if you're looking for PURE Vx (no other variables involved), you are looking at the maximum thrust vs. the lowest drag, provided by Vx0.
Regarding turbine aircraft, most are only certified for take-off with some flap deployed, so if you have to clear obstacles below acceleration altitude, you climb at Vx15 (e.g.), then accelerate & clean up after clearing the obstacles.
Brgds,
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