So for valuesofxclosetox 0 , the valuesofyof this tangentline will closelyapproximatef(x). This givesthe
approximation
The TangentLine Approximation(Linearization)
If f is a differentiablefunctionatx=x 0 , then the approximationfunctionis a linearizationoffnearx 0.Example1:
Find the linearizationof at pointx= 1.