The advancement of the second approximation is employed to introduce a modified version of the popular Secant technique, which is used to solve nonlinear optimization problems involving a single variable with no constraints. By utilizing the Taylor series expansion, an iterative formula is constructed, incorporating an approximation of l(c) second derivative. It is proven that these novel methods achieve quadratic convergence. when evaluated against the Newton technique using seven types of test function, A new approach performs well, as observed through real-world application.