Find f'(x) for f(x) = x^3 − 6x^2 + 9x, and identify the x-values of the critical points along with their nature.

• A. f'(x) = 3x^2 − 12x + 9; critical points x = 1 (local max) and x = 3 (local min)
• B. f'(x) = 3x^2 − 12x + 9; critical points x = 1 (local min) and x = 3 (local max)
• C. f'(x) = 3x^2 − 12x + 9; critical points x = −1 (local max) and x = 3 (local min)
• D. f'(x) = 3x^2 − 12x + 9; critical points x = 0 (critical) and x = 6 (critical)

Answer: (A)