Let \( f(x) = \begin{vmatrix} 3x^2 & \cos x & -\sin x \\ 6 & -1 & 0 \\ q & q^2 & q^3 \end{vmatrix} \) where \( q \) is any constant, then what is \( \frac{d^2}{dx^2}(f(x)) \) at \( x = 0 \) equal to ?

Explanation

Differentiating the first row twice gives (6, -\cos x, \sin x). At x = 0, this row becomes (6, -1, 0), making the first two rows of the determinant identical. A determinant with two identical rows evaluates to 0.

Related questions on Matrices & Determinants

• Consider the determinant \Delta=\begin{vmatrix}a_{11}&a_{12}&a_{13}\\ a_{21}&a_{22}&a_{23}\\ a_{31}&a_{32}&a_{33}\end{vmatrix} If $a_{13...
• If A=\begin{pmatrix}1&0&0\\ 0&\cos~\theta&\sin~\theta\\ 0&\sin~\theta&-\cos\theta\end{pmatrix}, then which of the following are correct?...
• If X is a matrix of order 3\times3, Y is a matrix of order 2\times3 and Z is a matrix of order 3\times2, then which of the follo...
• What is the value of a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}?
• What is the value of a_{21}C_{11}+a_{22}C_{12}+a_{23}C_{13}?