but,....velocity is a vector and in the case of a climb you have two components the forward component along the flight path and the vertical component,..with no other data [certification parameters or propeller advance ratio Vmc etc,...it can only said that at Vy you want the highest forward component of velocity along with a vertical component that is based on the amount of excess THP available for climb,..in order to obtain the highest forward component you'd want the highest IAS [TAS] i.e the highest 'V' possible and the greatest excess of THP and that would occur at Vimd in which you have the lowest drag there for the lowest thrust
required at the highest TAS possible giving the greatest difference between THPr and THPa,...
I think the question meant to say Vy not Vx as stated
old commentary on this:
Because at that point in a piston [a constant power variable thrust machine--as
Bookworm explained] you have the lowest drag coincident greatest possible lift coincident the only thing affecting climb rate as such is the difference between POWER required and POWER
available, however as the power falls off with altitude while drag is always equal to thrust....
But, ROC will decrease so to maintain the highest possible ROC [the condition required of Vx] at less power [from critical altitude] an increase in the lift term and therefore angle of attack is required this action induces drag and requires greater thrust maintain that new AOA at a constant altitude,...i.e there's less actual drag at altitude, but more drag required because more lift is required, so more thrust is required,...READ CAREFULLY THIS!!!
And, since power is thrust X Vtas and increase in velocity is required to maintain the required power for max climb angle,...
so in pistons Vx continually increases until it converges with Vy at the absolute performance altitude, whereas a jet produces constant thrust and a constant the AOA is that which produces the greatest climb rate i.e the AOA for L/Dmax
