Which of the following is the best linear approximation for f (x) = cos (x) near x = π/2

The local linear approximation of f near x = a is given by

f (x) ≈ f (a) + f' (a) (x-a)

Evaluating f at π/2

f (π/2) = cos (π/2) = 0

Since f (x) = cos (x), differentiating gets us

f' (x) = - sin (x)

f' (π/2) = - sin (π/2) = - 1

So the local liner approximation is

f (x) ≈ 0 + - 1 (x-π/2)

f (x) ≈ - x+π/2

The answer to this question is - x+π/2