Question

If f(x)= $\left|\begin{array}{ccc}1& 3\cos x& 1\\ \sin x& 1& 3\cos x\\ 1& \sin x& 1\end{array}\right|$, then which of the following is/are correct ?

• A. f(x) has maximum value $12$
• B. f(x) has maximum value $10$
• C. f (x) has maximum value $-10$
• D. f (x) has minimum value $0$

Answer 1

Answer: (B), (D)

The correct options are
B f(x) has maximum value $10$
D f (x) has minimum value $0$

$f\left(x\right)=8{\cos }^{2}x-3\sin 2x+1$ This can be written as
$f\left(x\right)=4\cos 2x-3\sin 2x+5$
Differentiating with respect to $x$ and simplifying gives us.
$\tan 2x=\frac{-3}{4}$ hence the sets of values will be
$\sin 2x=\frac{3}{5}$, $\cos 2x=\frac{-4}{5}$
or
$\sin 2x=\frac{-3}{5}$, $\cos 2x=\frac{4}{5}$
Therefore after substituting, we get the minimum and maximum values as $0$ and $10$ respectively.