Question

Find the linear approximation of the function
f(x) = square root of 1 − x
at a = 0.

Answer 1

L(x) = f(a) + f '(a)(x-a)

f(x) = sqrt(1- x)

f(a) = f(0) = 1

f '(x) = (1/2)(-1 / sqrt(1-x))

f '(a) = f '(0) = ?