Find the linear approximation of the function f(x) = √16-x at a = 0

Answer 1

What is a? It does not appear in your formula for f(x)

Do you mean
f(x) = (sqrt16) - x or sqrt(16-x)?

The first case is trivial: 4 -x.

For the second case, use the Taylor series formula.

At x=0, the derivative of f(x) is
f'(x) =
(-1/2)/(16-x)^1/2 = -1/8

In linear approximation,
f(x) = f(0) + f'(0)*x
= 4 - (x/8)