linear approximation calculus question

Question

The linear approximation at  x=0 to f(x) = (1)/(sqrt(8-x)) is

L(x) = A + Bx

where

A = ??

B = ??

Answer 1

L(x) = f(0) + f'(0)x = A + Bx

A=f(0) = 1/√8 = √8/8

f'(x) = 1/(2(8-x)^3/2)

B=f'(0) = 1/(2•8^3/2)

Answer 2

B= f'(0); f'(x) = [(8 - x)^-1/2]' = 1/2(8 - x)^-3/2; B = 1/2(8 - 0)^-3/2 = 1/(32√2); f(0) = 1/(2√2);

L(x) = f(0) + f'(0)(x - 0); L(x) = 1/(2√2) + 1/(32√2)x;

B = √2/64; A = √2/4