Let f(x) = x³ - 3x² + 6x - 10. Which of the following is true?

Let f(x) = x³ - 3x² + 6x - 10. Which of the following is true?

• A. f(x) is strictly increasing on R
• B. f(x) is strictly decreasing on R
• C. f(x) has a local maximum
• D. f(x) has a local minimum

Answer: A) f(x) is strictly increasing on R

Explanation: f'(x) = 3x² - 6x + 6 = 3(x² - 2x + 2). The discriminant of x² - 2x + 2 is 4 - 8 = -4 < 0. Thus f'(x) > 0 for all x ∈ R, meaning it is strictly increasing on R.