In this work,we propose a general procedure to achieve a class of optimal derivative free iterative methods using rational interpolant.The class is further extended to a general with memory family of iterative methods with increased order of convergence.We used a suitable variation of the two free parameters involved to increase the order of convergence from 2n to 2n+2(n-1)without any additional function evaluation.Hence,the with memory class retain better computational efficiency as compared to without memory methods.Numerical tests are presented to compare the performance of newly developed with and without memory families with the existing schemes of this domain which confirm robustness and efficiency of the presented families.