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Optimal eighth-order simple root-finders free from derivative

The calculation of derivatives of a function mostly takes up a great deal of time and even in some cases, such as the existing problems in engineering and optimization, is impossible to be evaluated directly. Accordingly, an accurate derivative-free class of three-step methods is suggested for solving f(x) = 0. The proposed three-step technique comprises four evaluations of the function per iteration. The analytical proof of the main contribution is given. And finally, the accuracy of the developed techniques is tested numerically by solving numerical examples.