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Show 20 The study of properties of functions generally involves finding "interesting" points of the function, that is those parameter values where the function does things it doesn't do everywhere else. There are several such interesting points, each of which has its own section below. Much of the study of biparametric functions is in terms of first and second order Taylor expansions of the functions The second order Taylor expansion of F(u,v) about about various points. The first order Taylor expansion of F(u,v) is: F(u,v) = F(uo,vo) + (U-uo)1 + (V-vo);1 , u , ,Vo Uo .v « This expansion approximates F by the planar function having the same postion and first derivatives at (uO,vO). (uO,vO) is aF aF F(u,v) = F(uo,vo) + (u-uo)au + (v-vo)av This approximates F by a quadratic function having the same value, first and second derivatives as F at (uO,vO). Stationay Points A particularly interesting point for univariate functions is the location of local maxima and minima. These occur at places where the first derivative of the function |
