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

Question

Anit [1.1K]

3 years ago

14

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?

Mathematics

1 answer:

sammy [17] · Answer 1 · 2022-03-25T02:21:31+03:00

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:

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​

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