If f(x) = |{2cos^4x, 2sin^4x, 3+sin^22x}, {3+2cos^4x, 2sin^4x, sin^22x}, {2cos^4x, 3+2sin^4x, sin^22x}| then

Question

If \(f(x)=\left|\begin{array}{ccc}2 \cos ^{4} x & 2 \sin ^{4} x & 3+\sin ^{2} 2 x \\ 3+2 \cos ^{4} x & 2 \sin ^{4} x & \sin ^{2} 2 x \\ 2 \cos ^{4} x & 3+2 \sin ^{4} x & \sin ^{2} 2 x\end{array}\right|\) then \(\frac{1}{5} f^{\prime}(0)\) is equal to _____

(1) 0

(2) 1

(3) 2

(4) 6

Answer 1

 Correct option is (1) 0

\(f(x) = \left|\begin{array}{ccc}2 \cos ^{4} x & 2 \sin ^{4} x & 3+\sin ^{2} 2 x \\ 3+2 \cos ^{4} x & 2 \sin ^{4} x & \sin ^{2} 2 x \\ 2 \cos ^{4} x & 3+2 \sin ^{2} 4 x & \sin ^{2} 2 x\end{array}\right|\)

\(f'(0) = 0 + 0 + 0 = 0\)

\(f'(0) = 0\) 

\(\frac 15.f'(0) = 0\)