Show that if f [a,b], then for , [a,b], there exists [a,b], so that f '( )=(f( )-f( )/( - ) )-(( - )/2) f''( )
To do this, do I have to show the proof? If so what is the proof?
Write out the Taylor expansion of about evaluated at , with remainder term for the series truncated after the first linear term (this will be in terms of the second derivative at some point in the interval if and if .
Now rearrange into the form:
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Last edited by CaptainBlack; Apr 11th 2010 at 12:43 AM.