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Application of Derivatives

Monotonicity

Premium Question

Grade 12

Question:

The function $f(x) = x^3 - 6x^2 + 9x + 18$ is strictly decreasing in the interval:

(1) $(1, 3)$

(2) $(-\infty, 1)$

(3) $(3,\infty)$

(4) $(-1, 1)$

Step-by-Step Solution

Key Concept: Differentiate $f$, factor $f'(x)$ completely, and determine on which interval(s) the factored expression is negative.

The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.

Correct Answer: (1)