The function f(x) = 2x³ - 3x² - 36x + 7 is strictly decreasing in the interval: A. (-∞, -2) B. (-2, 3) C. (3, ∞) D. (-3, 2) Answer: B) (-2, 3) Explanation: f'(x) = 6x² - 6x - 36 = 6(x² - x - 6) = 6(x - 3)(x + 2). For strictly decreasing, f'(x) < 0, which happens in the interval (-2, 3).

imo class 12 application of derivatives

The function f(x) = 2x³ - 3x² - 36x + 7 is strictly decreasing in the interval:

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The function f(x) = 2x³ - 3x² - 36x + 7 is strictly decreasing in the interval:

Answer: B) (-2, 3)

Explanation: f'(x) = 6x² - 6x - 36 = 6(x² - x - 6) = 6(x - 3)(x + 2). For strictly decreasing, f'(x) < 0, which happens in the interval (-2, 3).