I'm trying to understand this concept but the teacher kind of made it unclear.

The problem is

a. Sqrt(108)

b. Sqrt(1002)

For a. what the teacher did was:

a = 100 x = 8

F(x) = sqrt(x) F'(x) = 1/2sqrt(x)

Am I supposed to use the Linearlization formula to estimate this? Also why is a = 100 and x = 8?