Solution:
Takingthe derivativeoff(x),
we have , and
This tells us that near the pointx= 1, the function approximatesthe liney= (x/4) + 7/4.
As we moveawayfromx= 1, we lose accuracy(Figure9).
Example2:
Find the linearizationofy= sinxatx= π/3.
Solution:
Sincef(π/3)= sin(π/3)= , and we have