Module 5 : Linear and Quadratic  Approximations, Error  Estimates,  Taylor's Theorem,  Newton and Picard Methods
Lecture 14 : Quadratic approximations and error estimates [Section 14.2]
14.2.3
Corollary:
 

Let with and be the closed interval joining and . Let be such that

(i) The functions are all continuous.

(ii) For every between and ,
                       exists and ,
then satisfies the following:

                           

 

Proof:

Follows trivially from Taylor 's Theorem for .

   
 
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