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Let f(x) be the 3x3 determinant with rows [1 + sin² x, cos² x, 4 sin 2x], [sin² x, 1 + cos² x, 4 sin 2x], [sin² x, cos² x, 1 + 4 sin 2x]. Find the maximum value of f(x).
- 2
- 4
- 6
- 8
Correct answer: 6
Solution
Row reductions collapse the determinant to f(x) = 2 + 4 sin 2x, whose maximum (sin 2x = 1) is 6.
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