Question

If $f(x) = \begin{vmatrix} 2 \cos^4 x & 2 \sin^4 x & 3 + \sin^2 2x \\\ 3 + 2 \cos^4 x & 2 \sin^4 x & \sin^2 2x \\\ 2 \cos^4 x & 3 + 2 \sin^4 x & \sin^2 2x \end{vmatrix}$ then $\frac{1}{5} f'(0)$ is equal to

• A. 0
• B. 1
• C. 2
• D. 6

Answer 1

Answer: (A)

0

Answer 2

By simplifying the determinant using row operations:

$R_2 \rightarrow R_2 - R_1$, $R_3 \rightarrow R_3 - R_1$

we find that $f(x)$ is constant. Therefore, $f'(x) = 0$.

Thus,

$\frac{1}{5} f'(0) = 0$