Question

How can a linear approximation be used to approximate the value of a function f near a point at which f and f prime are easily​ evaluated?

Answer 1

Answer:

This can be solved by calculating a first degree Taylor approximation polynomial for the function in question around x=a. Taylor's first degree polynomial is given by:

$P_1(a) =f(a) +f'(a)(x-a)$

Through this expression, which is easily evaluable around the point x = a, the function f (x) is approximated through a linear function.

Step-by-step explanation: