If f(x) = x³ − 12x² + 36x + 17 is decreasing, then x belongs to: A. (2, 6) B. (−∞, 2) ∪ (6, ∞) C. (−∞, 2) D. (6, ∞) Answer: A) (2, 6) Explanation: f'(x) = 3x² − 24x + 36 = 3(x² − 8x + 12) = 3(x − 2)(x − 6). f'(x) < 0 → (x − 2)(x − 6) < 0 → 2 < x < 6.

imo class 12 application of derivatives

If f(x) = x³ − 12x² + 36x + 17 is decreasing, then x belongs to:

VAVidaara Admin Asked 6d ago 0 views 0 answers

If f(x) = x³ − 12x² + 36x + 17 is decreasing, then x belongs to:

Answer: A) (2, 6)

Explanation: f'(x) = 3x² − 24x + 36 = 3(x² − 8x + 12) = 3(x − 2)(x − 6). f'(x) < 0 → (x − 2)(x − 6) < 0 → 2 < x < 6.