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Step-by-Step Solution
Key Concept: The expression f(x) = \Sigma_{i=1}^3 \Sigma_{j=1}^3 a_{ij} c_{ij} is the expansion of the determinant \Delta(x) along any row or column, which is equal to the value of the determinant itself. Thus, f(x) = \Delta(x).
The expression f(x) = \Sigma_{i=1}^3 \Sigma_{j=1}^3 a_{ij} c_{ij} represents the value of the determinant \Delta(x). Expanding \Delta(x) along the first column: \Delta(x) = 0 - (x-1) * |2x-2 2x+8; 0 x+4| + 0 = -(x-1)(2x-2)(x+4) = -2(x-1)^2(x+4). For x \in [-3, 18], we analyze f(x) = -2(x-1)^2(x+4). Since (x-1)^2 \geq 0 and (x+4) \geq 1 for x \in [-3, 18], f(x) \leq 0. The maximum value is 0 at x = 1.
Correct Answer: 0