Slasher is very close to the mark here. V2min, at 1.2 Vs is, somewhat below the speed for best climb angle, but chosen and commonly used as a trade-off against improved field length performance. The best climb angle speed is typically a little above V2+10, and, if V2+10 has already been achieved, maintainance of V2+10 will achieve the best climb angle. Later generation aircraft have V2min derived as 1.13 Vs, and V2+15 is a better substitute for V2+10 for best angle for these aircraft.
An important point to remember is that following an engine failure below V2+10/15, the speed must not be allowed to increase. Using some of the much reduced excess thrust after engine failure for acceleration can only lead to reduced climb gradient, which may be critical if obstacle limited.
Where Operations manuals state that the speed following engine failure should be V2 to V2+10 (or V2 to V2+15), this is not "carte blanche" to operate at will within this speed band. Within this speed band, the existing speed should be maintained.
The overall summary (at least as far as I've written into various Operating Manuals is -
(1) If failure occurs below between V1 and V2, fly the approved pitch attitude to achieve V2, and then hold V2,
(2) If failure occurs between V2 and V2+10/15, hold the existing speed, e.g. V2+7,
(3) If failure occurs above V2+10/15, gently pitch up to reduce to V2+10/15, and hold V2+10/15.
(In the remarks above, the 10/15 would be either +10 or +15, depending upon the aircraft type, i.e. V2 = 1.2 Vs or 1.13 Vs).
In normal all-engines operations, we have the luxury of a large thrust excess, and simultaneous climb and acceleration may be safely conducted. With the much smaller thrust excess following engine failure, we may only use the excess thrust to Climb OR Accelerate, but not both. Certification depends upon this.
Regards,
Old Smokey