Derivatives Using Divided Difference Formula

we Obtain,

Substituting x = 1.6 in the formula

we obtain

Note :  Often, in applications, we require the maximum and/ or minimum of a function given as a tabulated data. We may obtain the interpolation polynomial, differentiate it and set it equal to zero to find the stationary points. Alternatively, we can use the numerical differentiation formula for finding the first derivative, set it equal to zero to find the stationary points. The numerical values obtained for the second derivatives at these stationary points decides whether there is a maximum or a minimum at these points.