KAG, what you're describing is called a zoom climb. It shouldn't be related to holding a Vx speed for a limited time. A zoom climb is not sustained like Vx and Vy are. During sustained climbs, mechanical work is being transferred into potential energy (altitude). In a zoom climb, it's typically done at full thrust/power and a majority of the aircraft's climb performance is from it's kinetic energy being converted into potential energy (altitude).