The function f(x) = x³ − 3x² + 3x − 100 is strictly:

The function f(x) = x³ − 3x² + 3x − 100 is strictly:

• A. Increasing for all x ∈ R
• B. Decreasing for all x ∈ R
• C. Increasing for x > 1 only
• D. Decreasing for x < 1 only

Answer: A) Increasing for all x ∈ R

Explanation: f'(x) = 3x² − 6x + 3 = 3(x − 1)² ≥ 0 for all x. Since f'(x) is never negative, f is strictly increasing on R (except at x = 1 where derivative is zero but function is still increasing overall).