Calculus homework question

Question

Compute the Taylor polynomial of degree 2 about 1 for function f(x) = sin(2x).

Answer 1

P₂(x) = f(1) + f'(1)(x-1) + (f"(1)/2)(x-1)²

f(x) = sin(2x), so f(1) = sin2 ≈ 0.909 (make sure that your calculator is in radian mode)

f'(x) = 2cos(2x), so f'(1) = 2cos2 ≈ -0.832

f"(x) = -4sin(2x), so f"(1) / 2 = -4sin2 ≈ -1.818

P₂(x) ≈ 0.909 - 0.832(x-1) - 1.818(x-1)²