Let f(x) = |3x² cos x −sin x ; 6 −1 0 ; q q² q³| where q is any constant, then what is d²/dx²(f(x)) at x = 0 equal to?

Expanding the determinant along row 2: f(x) = −6[cos x · q³ − (−sin x)·q²] + (−1)[3x²·q³ − (−sin x)·q] · (−1) ... More cleanly: f(x) = 3x²·(−q³ − 0) − cos x·(6q³ − 0) + (−sin x)·(6q² − (−q)) = −3q³ x² − 6q³ cos x − sin x(6q² + q). Then f''(x) = −6q³ + 6q³ cos x + sin x(6q² + q). At x = 0: f''(0) = −6q³ + 6q³ + 0 = 0.