For f(x) = x^3 − 9x, identify the critical points and their nature.

• A. f'(x) = 3x^2 − 9; critical points x = −√3 (local max) and x = √3 (local min)
• B. f'(x) = 3x^2 − 9; critical points x = −√3 (local min) and x = √3 (local max)
• C. f'(x) = 3x^2 − 9; critical points x = 0 and x = 3
• D. f'(x) = 3x^2 − 9; critical points x = 1 and x = −1

Answer: (A)