The paper employs Lagrange's mean value theorem of differential Calculus to design a new strategy for the selection of parameter vectors in the Differential Evolution (DE) algorithm. Classical differential evolution selects parameter vectors randomly to obtain the donor vectors. These donor vectors thus cannot be directly used as trial solution to the optimization problem. The recombination step indeed is very useful to generate potential trial solutions. The proposed algorithm eliminates the recombination step as the trial solutions can be directly generated by the extended mutation step only. Performance analysis of the proposed algorithm with respect to standard benchmark functions reveals that both in expected convergence time and accuracy in solutions, the proposed algorithm outperforms classical DE/rand/1. Besides extension in mutation strategy, an adaptive selection strategy in the scaling factor F also improves the performance of the proposed algorithm. In addition, the proposed algorithm outperforms classical DE in noisy optimization problem. Further, the number of function evaluation with scaled up dimensions of the optimization problem adds insignificantly small complexity in comparison to that in classical differential evolution to meet up a prescribed level of accuracy in solution quality.