the secant method the secant method when finding the derivative xin newton' method is problematicor when function evaluations take too longwe may adjust the method slightly instead of using tangent lines to the graph we may use secants the approach is referred to as the secant methodand the idea is illustrated graphically in fig for our example problem the idea of the secant method is to think as in newton' methodbut instead of using xn /we approximate this derivative by finite difference or the secanti the slope of the straight line that goes through the points xn xn /and xn xn /on the graphgiven by the two most recent approximations xn and xn this slope reads xn xn ( xn xn inserting this expression for xn in newton' method simply gives us the secant methodf xn xnc xn / xn xn or xnc xn xn xn xn xn xn ( fig illustrates the use of secants in the secant method when solving oe from two chosen starting valuesx and the crossing of the corresponding secant with the axis is computedfollowed by similar computation of from and