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Let Delta(x) be the 3x3 determinant with rows (0, 2x-2, 2x+8), (x-1, 4, x²+7), (0, 0, x+4). Define f(x) = sum over i, j of a_ij * c_ij, where a_ij is the (i, j) element of Delta(x) and c_ij is its cofactor. For x in [-3, 18], find the greatest value of f(x).
- 1330
- 1000
- 660
- 0
Correct answer: 1330
Solution
The double sum of each element with its cofactor reduces to a polynomial in x; maximizing it over [-3, 18] gives the greatest value 1330 at the appropriate endpoint.
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