Find the intervals in which the following functions are strictly increasing or decreasing:
x² + 2x - 5
Strictly decreasing in (-∞, -1); Strictly increasing in (-1, ∞)
10 - 6x - 2x²
Strictly increasing in (-∞, -3/2); Strictly decreasing in (-3/2, ∞)
-2x³ - 9x² - 12x + 1
Strictly decreasing in (-∞, -2) and (-1, ∞); Strictly increasing in (-2, -1)
6 - 9x - x²
Strictly increasing in (-∞, -9/2); Strictly decreasing in (-9/2, ∞)
(x + 1)³ (x - 3)³
Strictly decreasing in (-∞, 1); Strictly increasing in (1, ∞)
Explanation
This question tests the application of derivatives to determine intervals of monotonicity. The key method involves finding critical points where f'(x) = 0, then analyzing the sign of f'(x) in different intervals. A function is strictly increasing where f'(x) > 0 and strictly decreasing where f'(x) < 0. The textbook demonstrates this approach in Example 11, showing how to divide the real line into intervals using critical points and determine the nature of the function in each interval.