A differentiable function f(x) has a local maximum at x = 0. Let y = 2f(x) + ax - b. Which of the following is/are correct? 1. f'(0) = 0. 2. f''(0) < 0. Select the correct answer using the code given below:

Since f(x) has a local maximum at x = 0 and f is differentiable, by Fermat's theorem f'(0) = 0. For a local maximum of a twice-differentiable function, the second derivative test gives f''(0) ≤ 0. Generally for a strict local maximum f''(0) < 0 (assuming non-degenerate case). Both statements are correct.