IND ENG 160 Lecture Notes - Lecture 6: Taylor Series, Maxima And Minima

• School: Berkeley
• Department: Industrial Engineering And Operations Research
• Course: IND ENG 160
• Professor: Javad Lavaei

Document Summary

The taylor series approximation estimates a function by a series of monomials involving the derivative of f (x). It is arbitrarily accurate, as it is an in nite series. f 2(x ) x2 + . If our function is f (x) = ex, our approximation is f (x + x) = f (x ) + f (x ) x + e x = 1 + x + We had factored out an ex from every term in this in nite series. Suppose f (x) = ex1+x2 , and we have x = (cid:20)0. We get a vector for our rst derivative, and a matrix (the hessian) for the second derivative. f (x + x) = f (x ) + f (x ) x + The form xt ax turns a matrix into a scalar by multiplication with x. We have new de nitions for de nite and semide nite matrices.