JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(f(x)=\left|\begin{array}{ccc}x^3 & 2 x^2+1 & 1+3 x \\ 3 x^2+2 & 2 x & x^3+6 \\ x^3-x & 4 & x^2-2\end{array}\right|\) for all \(x \in \mathbb{R}\), then \(2 f(0)+f^{\prime}(0)\) is equal to
- A \(48\)
- B \(24\)
- C \(42\)
- D \(18\)
Answer & Solution
Correct Answer
(C) \(42\)
Step-by-step Solution
Detailed explanation
\(\mathrm{f}(0)=\left|\begin{array}{ccc}0 & 1 & 1 \\ 2 & 0 & 6 \\ 0 & 4 & -2\end{array}\right|=12\) \(f^{\prime}(x)=\left|\begin{array}{ccc}3 x^2 & 4 x & 3 \\ 3 x^2+2 & 2 x & x^3+6 \\ x^3-x & 4 & x^2-2\end{array}\right|+\)…
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