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