Dynamic voltage and frequency scaling (DVFS) is considered one of the most efficient techniques for reducing energy consumption. Our studies have found that the optimal operation speed with optimal energy efficiency typically achieves when the processor running at a specific speed other than the lowest speed. Additionally, there exists an inverse relationship between the memory access rate (MAR) and the frequency that can minimize the energy consumption. Therefore, a predictive model can be deduced from the memory access rate to determine a frequency that tends to minimize the CPU energy consumption. In this paper, the existence of a critical speed and the memory access rate-critical speed equation (MAR-CSE) is proved theoretically and practically. A lower bound for Dynamic Voltage and Frequency Scaling is also defined. We report the most energy-efficient DVFS model that provide upper bounds of the reduction of energy consumption. The proposed approach has been implemented on embedded Linux operating system. The experimental results on energy consumption analysis show that our algorithm outperforms other existent DVFS algorithms.