If I'm correct in my assumptions this should mean that the highest rate of climb is reached when you climb at minimum clean speed. This would mean minimum amount of resistance from the air and maximum amount of energy used to climb.
Think you are confusing max rate of climb with max
angle of climb - not the same thing! Former is height gained v time whereas latter is height gained v horizontal distance travelled.
Best rate of climb is achieved where the gap between power required and power available is largest!
Of course it also makes a difference whether it's jet or piston - if you want a good explanation see Mechanics of Flight by A.C. Kermode - one of the classics!