Show that the equation 
has a root in the interval 
and use Newton's Method to approximate it with an error of at most 
.
Definitions:
Vildagliptin
A medication used to manage type 2 diabetes by increasing insulin release and decreasing glucagon production.
Antidiabetic Drug
A medication used to manage and treat diabetes by controlling blood sugar levels.
Functional Group
A specific grouping of atoms within molecules that have characteristic chemical reactions regardless of the molecules they are part of.
Structurally Isomeric
Pertains to molecules that have the same molecular formula but feature different physical structures.
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